Optimization Books

Book SynopsisIntroduction.- Iterative methods.- Methods with remotest set control.- Set-valued inclusions.- The Cimmino algorithm in a normed space.- Dynamic string-averaging methods.- References.

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Book SynopsisPreface.- Part I. An Introduction to Inverse Combinatorial Optimization Problems.- An Outline of Inverse Combinatorial Optimization Problems.-  Generalized Inverse Bottleneck Optimization Problems.- Generalized Inverse Maximum Capacity Path Problems.- Some General Methods to Solve Inverse Linear Programming Problem under Weighted ??1 Norm.- Part II. Generalized Inverse Shortest Path Problems.- Shortest Path Improvement Problems.- Shortest Path Interdiction Problems on Trees.- Sum of Root-leaf Distance Interdiction Problems on Trees.- Restricted Inverse Optimal Value Problem on Shortest Path under Weighted ??1 Norm on Trees.- Part III. Generalized Inverse Spanning Tree Problems.- Inverse Minimum Spanning Tree Problems.- Inverse Max+Sum Spanning Tree Problems.- Restricted Inverse Optimal Value Problem on Minimum Spanning Tree.- Partial Inverse Minimum Spanning Tree Problems.- Part IV. Generalized Inverse Center Location Problems.- Inverse vertex obnoxious 1-center location problems.- Inverse Quickest 1-Center Location Problem on Trees.- References.

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Book Synopsis.- A Case Study on Stochastic Security-Constrained Unit Commitment for Power Systems Models in Baden-W¨urtemberg..- New centrality indices in network analysis..- On Variants of PCGs: A Survey of Current Results and Open Problems.Simulation Experiments to Assess the Effectiveness of Randomization in Security Screening at Sports and Entertainment Venues..- Sentiment and Conflict Prediction in Urban Development: Data-Driven Approach..- Advanced Last-Mile Delivery: A Review of Truck-Drone and Multi-Vehicle Fleet Systems for Sustainable Logistics..- Flexible Pooling Pattern Design with Integer Programming..- Formulations of the Currency Portolio Optimization Problem and Sensitivity Analysis of a Currency Basket..- On the consistency and large deviations of the method of empirical means in stochastic programming problems..- Automatic tuning of the Skewed Kruskal algorithm..- Approximating the feasible criterion set in multi-criteria optimization problems described by equations in par??al derivatives..- The (In)Famous Big-M Technique for Solving Bi-level Programs..- Optimization Techniques for Twin Support Vector Machines in Primal Space..- On the calculation of similarity measures for figures by nonsmooth global optimization..- Approximating multicriteria matrix game solution with finite sets..- Optimization of an e-commerce supply chain: middle-mile and last-mile..- Unified Presentation of the Generalized Ellipsoid Method..- Non-submodular Optimization and Nonconvex Relaxation..- DR-submodular maximization and its application..- Optimization of the design and control of an optical system with structural inhomogeneities.

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Book SynopsisPreface.- Introduction.- Convex sets and convex functions.- Subgradient and mirror descent methods.- Proximal algorithms.- Karush-Kuhn-Tucker theory and Lagrangian duality.- ADMM: alternating direction method of multipliers.- Primal dual splitting algorithms.- Error bound conditions and linear convergence.- Optimization with Kurdyka- Lojasiewicz property.- Semismooth Newton methods.- Stochastic algorithms.- References.- Index.

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Book Synopsis.- Introduction..- Basic Facts of Set Theory..- Linear Spaces..- Rudiments of General Topology..- Filters: the Fifth Equivalence..- Hahn Banach andSeparation Theorems..- Locally Convex and Barrelled Spaces..- Metrics and pseudometrics, Norms and Pseudonorms..- Topological Form of Hahn Banach and Separation Theorems..- Extreme points, Faces, Support and the KreinMilman Theorem..- Function Spaces.

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Book SynopsisMathematical Programming.- Adaptive Variants of Frank-Wolfe Method with Relative Inexact Gradient Information.- Construction of a self-concordant barrier for a quasi-polyhedral cone with infinitely many faces.- Adaptive Method for Saddle Point Problems with a Generalization of Smoothness Property.- On the Study of Some Sufficient Conditions for the Existence of Regular Zeros of Quadratic Mappings.- STOCHASTIC GRADIENT DESCENT METHODS WITH STEP ADAPTATION.- Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers.- Optimal Control.- On a Problem of Synthesis of Control of Boundary Condition and Motion of Measurement Points for Damping Oscillations of a String.- The Problem of Synthesis of Control of Movement of State Sensors and Power of Heating Sources of the Rod with Optimization of Their Placement.- On the Optimality of the Guaranteeing Solution in the Time-Optimization Problem for Linear Discrete-Time Systems with Integral Control Constraints.- Discrete H2-Optimal Synthesis Problem with Nonunique Solution.- Scattering-based stabilization technique for QSR-dissipative teleoperators with time-varying communication delays.- Game Theory.- Time-Inconsistency of Cooperative Networks in Differential Games.- Complete-to-Sparse: A Novel Graph Construction Strategy to Increase Efficiency of ShapG.- Two-Stage Game Model of Opinion Dynamics.- Genetic Algorithm for Repeated Prisoner's Dilemma.- Operations Research and Applications.- BIGLDM: Innovative Forecasting of Infection Patterns with Bidirectional Generalized Least Deviation Models.- Closest target on the frontier of the free disposal hull.- Optimal trajectory for monitoring objects with obstacles.- An Improved Discrete Optimisation Procedure with comparison to Constraint Programming.- On a Bilevel Optimization Model of Electric Power Systems with a System Operator at the Upper Level.- Multivariate Selberg Probability Bound in Distributionally Robust Optimization with Statistical Applications.- MIP Models and Complexity Results for DAG Scheduling in the Cloud.- Machine Learning and Optimization.- Clustering-based Graph Neural Networks in a Weakly Supervised Regression Problem.- Heterogeneous graph neural networks for real-time flow assignment prediction.- A Nash Equilibrium Prediction for a Dual Market Economic System Using Machine Learning Methods.- Parameter optimization for restarted mixed precision iterative sparse solver.- Optimal collapsing levels in one-way ANOVA: agglomerative merging algorithms and mixed integer linear programming.

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Book SynopsisPreface.- Introduction.- MISO-AGP: dealing with multiple information sources via Augmented Gaussian Process.- MISO-AGP in action: selected applications.- Bayesian Optimization and Large Language Models.- References.

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Book SynopsisThis book may serve as a basis for students and teachers. The text should provide the reader with a quick overview of the basics for Optimal Control and the link with some important conceptes of applied mathematical, where an agent controls underlying dynamics to find the strategy optimizing some quantity. There are broad applications for optimal control across the natural and social sciences, and the finale to this text is an invitation to read current research on one such application. The balance of the text will prepare the reader to gain a solid understanding of the current research they read.

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Book SynopsisThis book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics", and is organized as a short presentation of few important points on the arguments indicated in the title. It aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. Prerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography. In conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE

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Book SynopsisThe purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.Trade Review“In this small book, the author, after introducing basic and non-basic concepts of the theory of viscosity solutions for first and second order PDEs, applies the theory to two specific problems such as existence of viscosity solution for the Euler-Lagrange PDE and for the ∞-Laplacian. … The book can be certainly used as text for an advanced course and also as manual for researchers.” (Fabio Bagagiolo, zbMATH, Vol. 1326.35006, 2016)“The book under review is a nice introduction to the theory of viscosity solutions for fully nonlinear PDEs … . The book, which is addressed to a public having basic knowledge in PDEs, is based on a course given by the author … . The explanations are very clear, and the reader is introduced to the theory step by step, the author taking the time to explain several technical details, but without making the exposition too heavy.” (Enea Parini, Mathematical Reviews, November, 2015)Table of Contents1 History, Examples, Motivation and First Definitions.- 2 Second Definitions and Basic Analytic Properties of the Notions.- 3 Stability Properties of the Notions and Existence via Approximation.- 4 Mollification of Viscosity Solutions and Semi convexity.- 5 Existence of Solution to the Dirichlet Problem via Perron’s Method.- 6 Comparison results and Uniqueness of Solution to the Dirichlet Problem.- 7 Minimisers of Convex Functionals and Viscosity Solutions of the Euler-Lagrange PDE.- 8 Existence of Viscosity Solutions to the Dirichlet Problem for the Laplacian.- 9 Miscellaneous topics and some extensions of the theory.

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Book SynopsisThis work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.Trade Review“This short book is dedicated to convex optimization, beginning with theoretical aspects, ending with numerical methods, and complemented with numerous examples. … this is an interesting and well-written book that is adequate for a graduate-level course on convex optimization.” (Constantin Zălinescu, Mathematical Reviews, November, 2015)Table of ContentsBasic Functional Analysis.- Existence of Minimizers.- Convex Analysis and Subdifferential Calculus.- Examples.- Problem-solving Strategies.- Keynote Iterative Methods.

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Book SynopsisPresenting a practitioner's guide to capabilities and best practices of quality control systems using the R programming language, this volume emphasizes accessibility and ease-of-use through detailed explanations of R code as well as standard statistical methodologies. In the interest of reaching the widest possible audience of quality-control professionals and statisticians, examples throughout are structured to simplify complex equations and data structures, and to demonstrate their applications to quality control processes, such as ISO standards. The volume balances its treatment of key aspects of quality control, statistics, and programming in R, making the text accessible to beginners and expert quality control professionals alike. Several appendices serve as useful references for ISO standards and common tasks performed while applying quality control with R. Trade Review Table of Contents

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Book SynopsisThis clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background. Trade Review“This is a friendly and well-written introduction to a topic of great interest in modern analysis.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 193 (4), 2020)“This book is an introductory textbook … . The textbook is appropriate for students with solid background in calculus and linear algebra but without preliminary knowledge of variational analysis. … this textbook is useful for beginning graduate students in physical, engineering, and mathematical sciences having a rigorous theoretical background.” (Mihail Voicu, zbMATH 1390.49001, 2018)Table of ContentsIntroduction.- The Euler-Language Equation.- Variational Problems with Constraints.- Direct Methods in the Calculus of Variations.- Appendix.- Solutions of the Exercises.

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Book SynopsisThis volume contains selected papers presented at the International Conference on Operations Research SOR 2002 held at the University of Klagenfurt from Sep- tember 2 to September 5, 2002. The conference was organized under the auspices of the German, the Swiss and the Austrian Operations Research societies - Gesellschaft fiir Operations Research e.V. (GOR) - Schweizerische Vereinigung fiirOperations Research (SVOR) - Osterreichische Gesellschaft fiirOperations Research (OGOR). After Vienna (1990), Berlin (1994) and Ziirich (1998) this has been the fourth time that the three societies organized ajoint conference. The conference was attended by more than 400 participants from countries all over the world which demonstrates the broad interest in all aspects ofOperations Research. The scientific program of the conference consisted of 4 plenary lectures, 5 semi plenary lectures, and about 320 contributed papers which have been presented in 16 sections. Due to the limited number of pages available for the proceedings vol- ume, the length of each article as well as the total number ofcontributions had to be restricted. The decision on the acceptance of papers for the proceedings has been made in close eo operation with the section chairmen and was based on their suggestions. We wish to express our sincere thanks to the chairmen for supporting our editorial work by refereeing the manuscripts and letting us have their advice. We also would like to thank Dr. Wemer Muller from Springer-Verlag for his support in publishing this proceedings volume so quickly.Table of ContentsThe Role of Operations Research in Public Policy.- Risk-Return Optimization of the Bank Portfolio.- Resource-orientated Purchase Planning and Supplier Selection - Models and Algorithms for Supply Chain Optimization and E-Commerce.- A Combinatorial Approach to Orthogonal Placement Problems.- Assigning Frequencies in GSM Networks.- Optimal Control of Methadone Treatment in Preventing Blood-Borne Disease.- Strategien zur Rüstzeitvermeidung in der Elektronikfertigung.- Optimale Belegung von Stranggießanlagen mittels 2-dimensionaler Bin-Packing-Modelle.- Short-term Capacity Planning in Manufacturing Companies with a Decentralized Organization.- Performance Analysis of Make to Stock Supply Chains Using Discrete-Time Queueing Models.- A New Optimal Demand Forecast Model.- A Multi-Product Batch-Available-to-Promise Model for Make-to Stock Manufacturing.- Scheduling of Rolling Ingots Production.- Determination of Economic Production Quantity for a Multi-Stage Production System with Limited Storage Capacity.- A Reverse Logistics Model with Integer Setup Numbers.- Lotsizing in a Production System with Rework and Product Deterioration.- Mathematical Programming Models for Strategic Supply Chain Planning and Design.- Ein dynamisches Verhandlungsmodell des Supply Chain Management.- Modeling the Interaction between Operational and Financial Decisions in the Inventory Pooling of Repairable Spare Parts Problem.- Die Schätzung von Markentreue, Nichtkäuferanteil und Marktpotenzial aus Handelspaneldaten.- A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem.- Online-Algorithmus zur Steuerung von Verkehrslichtsignalanlagen.- Optimal Sorting Machine Allocation in the Postal Distribution Network.- A Combined Approach to Solve the Pickup and Delivery Selection Problem.- VRP with Interdependent Time Windows - A Case Study for the Austrian Red Cross Blood Program.- Incident Management Based on Real Time Simulation.- Online-Dispatching of Automobile Service Units.- Multi-Class User Equilibria under Social Marginal Cost Pricing.- School Bus Rooting and Scheduling Problem.- Covering Population Areas by Railway Stops.- Innovative Lösungen im bimodalen Transport Straße I Binnenstraße.- Optimal Routing of Snowplows - A Column Generation Approach.- Savings Based Ants for Large-scale Vehicle Routing Problems.- Single Machine Scheduling Problems with Exponentially Start Time Dependent Job Processing Times.- Scheduling Problems with Optimal Due Interval Assignment Subject to Some Generalized Criteria.- A New Exact Resource Allocation Model with Hard and Soft Ruource Constraints.- Minimizing Total Weighted Tardiness on Parallel Batch Process Machinu Using Genetic Algorithms.- Sorting with Line Storage Systems.- On Solvability of the Project Scheduling Problem with Accumulative Resources of an Arbitrary Sign.- Cost Optimized Layout of Fibre Optic Networks In the Access Net Domain.- Ein Algorithmus zur sicheren elektronischen Stimmabgabe Ober das Internet.- Accelerated MILP-Strategies for the Optimal Operation Planning of Energy Supply System.- On On-line Systems for Short-term Forecasting for Energy Systems.- Combining Bottom-up and Finance Modelling for Electricity Markets.- Gestaltung von Stoffstrom-Netzwerken zum Produktrecycling.- Ein Ansatz zur Bewertung von Remanufacturingstrategien.- Environmental Coordination of Supply Chain Networks Based on a Multi-Agent System.- Decision Support for the National Implementation of Emission Reduction Measures by the Dynamic Mass Flow Optimisation Model ARGUS.- Fuzzy Scheduling for the Dismantling of Complex Products.- Group Decision Making Versus Expert Opinion in the Multi-Objective Analysis of Ecosystem Management.- Capital Market Efficiency - An Empirical Analysis of the Dividend Announcement Effect for the Austrian Stock Market.- On Tail Index Estimation and Financial Risk Management Implications.- Project Risk Management by a Probabilistic Expert System.- Regulatory Impacts on Credit Portfolio Management.- Verfahren zur Risikokapitalallokation im Eigenhandel von Banken.- Process Optimization via Conventional Factorial Designs and Simulated Annealing on the Path of Steepest Ascent for a CSTR.- Optimization on Directionally Convex Sets.- Meta-Heuristiken in Virtuellen Lernumgebungen.- An Evolutionary Algorithm for Bayesian Network Triangulation.- Approximation Algorithms for the k-center Problem: An Experimental Evaluation.- MaxFlow-MinCut Duality for a Paint Shop Problem.- From Edge Decomposition Formulae to Composition Algorithms.- The Complexity of Some Problems on Maximal Independent Sets in Graphs.- Testing Solution Quality in Stochastic Programs.- Scenario Updating Method for Stochastic Mixed-integer Programming Problems.- Pricing of Multidimensional Resources in Revenue Management.- A Note on Quantitative Stability and Empirical Estimates in Stochastic Programming.- Splitting and Localization of the Epi-Topology Combined with Randomness.- Standards für Modellierung und Simulation.- System Dynamics(SD) - An Approach within Corporate Plannning.- Optimal Decision Rules in a Monetary Union.- Impact of Feedback Loop on Group Decision Process when Applying System Dynamics Simulators.- The Management Game SINTO-Market - Report on Some Recent Experiments.- Bounds & Likelihood Procedure Revisited.- On the Allocation of Excesses of Resources in Linear Production Problems.- Simulation eines CO2-Zertifikatenhandels und algorlthmische Optimierung von Investitionen.- Indirect Expenditure Functions and Shephard’s Lemma.- Bayesian Estimation of the Heston Stochastic Volatility Model.- Forecasting with Leading Economic Indicators - A Neural Network Approach.- Estimating Multivariate Conditional Distributions - An Application to the Truck Sales Forecast.- Application of Techniques of Functional Data Analysis to Spectroscopic Data.- Integrating Exchange Rate Theory in Data Mining.- The Ability of Artificial Neural Networks to Exploit Non-Linearitles by Data Mining Models Compared to Statistical Methods.- Preference Measurement with Conjoint Analysis and AHP: An Empirical Comparison.- Further Development of MADM-Approaches in China and in Germany.- Wissensrevision in einer MaxEnt/MinREnt-Umgebung.- Innovation, Operations Research & Decision Support In the Military.- Von der Prädlkatenloglk zur unternehmerischen Entscheidungsunterstützung.

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Book SynopsisFrom the reviews: "[…] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. […] I can recommend it for any mathematician or physicist interested in this field." Zentralblatt MATHTrade Review"The monograph by T. Kato is an excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.In chapters 1, 3, 5 operators in finite-dimensional vector spaces, Banach spaces and Hilbert spaces are introduced. Stability and perturbation theory are studied in finite-dimensional spaces (chapter 2) and in Banach spaces (chapter 4). Sesquilinear forms in Hilbert spaces are considered in detail (chapter 6), analytic and asymptotic perturbation theory is described (chapter 7 and 8). The fundamentals of semigroup theory are given in chapter 9. The supplementary notes appearing in the second edition of the book gave mainly additional information concerning scattering theory described in chapter 10.The first edition is now 30 years old. The revised edition is 20 years old. Nevertheless it is a standard textbook for the theory of linear operators. It is user-friendly in the sense that any sought after definitions, theorems or proofs may be easily located. In the last two decades much progress has been made in understanding some of the topics dealt with in the book, for instance in semigroup and scattering theory. However the book has such a high didactical and scientific standard that I can recomment it for any mathematician or physicist interested in this field.Zentralblatt MATH, 836Table of ContentsOne Operator theory in finite-dimensional vector spaces.- § 1. Vector spaces and normed vector spaces.- 1. Basic notions.- 2. Bases.- 3. Linear manifolds.- 4. Convergence and norms.- 5. Topological notions in a normed space.- 6. Infinite series of vectors.- 7. Vector-valued functions.- § 2. Linear forms and the adjoint space.- 1. Linear forms.- 2. The adjoint space.- 3. The adjoint basis.- 4. The adjoint space of a normed space.- 5. The convexity of balls.- 6. The second adjoint space.- § 3. Linear operators.- 1. Definitions. Matrix representations.- 2. Linear operations on operators.- 3. The algebra of linear operators.- 4. Projections. Nilpotents.- 5. Invariance. Decomposition.- 6. The adjoint operator.- § 4. Analysis with operators.- 1. Convergence and norms for operators.- 2. The norm of Tn.- 3. Examples of norms.- 4. Infinite series of operators.- 5. Operator-valued functions.- 6. Pairs of projections.- § 5. The eigenvalue problem.- 1. Definitions.- 2. The resolvent.- 3. Singularities of the resolvent.- 4. The canonical form of an operator.- 5. The adjoint problem.- 6. Functions of an operator.- 7. Similarity transformations.- § 6. Operators in unitary spaces.- 1. Unitary spaces.- 2. The adjoint space.- 3. Orthonormal families.- 4. Linear operators.- 5. Symmetric forms and symmetric operators.- 6. Unitary, isometric and normal operators.- 7. Projections.- 8. Pairs of projections.- 9. The eigenvalue problem.- 10. The minimax principle.- Two Perturbation theory in a finite-dimensional space.- § 1. Analytic perturbation of eigenvalues.- 1. The problem.- 2. Singularities of the eigenvalues.- 3. Perturbation of the resolvent.- 4. Perturbation of the eigenprojections.- 5. Singularities of the eigenprojections.- 6. Remarks and examples.- 7. The case of T(x) linear in x.- 8. Summary.- § 2. Perturbation series.- 1. The total projection for the ?-group.- 2. The weighted mean of eigenvalues.- 3. The reduction process.- 4. Formulas for higher approximations.- 5. A theorem of Motzkin-Taussky.- 6. The ranks of the coefficients of the perturbation series.- § 3. Convergence radii and error estimates.- 1. Simple estimates.- 2. The method of majorizing series.- 3. Estimates on eigenvectors.- 4. Further error estimates.- 5. The special case of a normal unperturbed operator.- 6. The enumerative method.- § . Similarity transformations of the eigenspaces and eigenvectors.- 1. Eigenvectors.- 2. Transformation functions.- 3. Solution of the differential equation.- 4. The transformation function and the reduction process.- 5. Simultaneous transformation for several projections.- 6. Diagonalization of a holomorphic matrix function.- § 5. Non-analytic perturbations.- 1. Continuity of the eigenvalues and the total projection.- 2. The numbering of the eigenvalues.- 3. Continuity of the eigenspaces and eigenvectors.- 4. Differentiability at a point.- 5. Differentiability in an interval.- 6. Asymptotic expansion of the eigenvalues and eigenvectors.- 7. Operators depending on several parameters.- 8. The eigenvalues as functions of the operator.- § 6. Perturbation of symmetric operators.- 1. Analytic perturbation of symmetric operators.- 2. Orthonormal families of eigenvectors.- 3. Continuity and differentiability.- 4. The eigenvalues as functions of the symmetric operator.- 5. Applications. A theorem of Lidskii.- Three Introduction to the theory of operators in Banach spaces.- § 1. Banach spaces.- 1. Normed spaces.- 2. Banach spaces.- 3. Linear forms.- 4. The adjoint space.- 5. The principle of uniform boundedness.- 6. Weak convergence.- 7. Weak* convergence.- 8. The quotient space.- § 2. Linear operators in Banach spaces.- 1. Linear operators. The domain and range.- 2. Continuity and boundedness.- 3. Ordinary differential operators of second order.- § 3. Bounded operators.- 1. The space of bounded operators.- 2. The operator algebra ?(X).- 3. The adjoint operator.- 4. Projections.- § 4. Compact operators.- 1. Definition.- 2. The space of compact operators.- 3. Degenerate operators. The trace and determinant.- § 5. Closed operators.- 1. Remarks on unbounded operators.- 2. Closed operators.- 3. Closable operators.- 4. The closed graph theorem.- 5. The adjoint operator.- 6. Commutativity and decomposition.- § 6. Resolvents and spectra.- 1. Definitions.- 2. The spectra of bounded operators.- 3. The point at infinity.- 4. Separation of the spectrum.- 5. Isolated eigenvalues.- 6. The resolvent of the adjoint.- 7. The spectra of compact operators.- 8. Operators with compact resolvent.- Four Stability theorems.- §1. Stability of closedness and bounded invertibility.- 1. Stability of closedness under relatively bounded perturbation.- 2. Examples of relative boundedness.- 3. Relative compactness and a stability theorem.- 4. Stability of bounded in vertibility.- § 2. Generalized convergence of closed operators.- 1. The gap between subspaces.- 2. The gap and the dimension.- 3. Duality.- 4. The gap between closed operators.- 5. Further results on the stability of bounded in vertibility.- 6. Generalized convergence.- § 3. Perturbation of the spectrum.- 1. Upper semicontinuity of the spectrum.- 2. Lower semi-discontinuity of the spectrum.- 3. Continuity and analyticity of the resolvent.- 4. Semicontinuity of separated parts of the spectrum.- 5. Continuity of a finite system of eigenvalues.- 6. Change of the spectrum under relatively bounded perturbation.- 7. Simultaneous consideration of an infinite number of eigenvalues.- 8. An application to Banach algebras. Wiener’s theorem.- § 4. Pairs of closed linear manifolds.- 1. Definitions.- 2. Duality.- 3. Regular pairs of closed linear manifolds.- 4. The approximate nullity and deficiency.- 5. Stability theorems.- § 5. Stability theorems for semi-Fredholm operators.- 1. The nullity, deficiency and index of an operator.- 2. The general stability theorem.- 3. Other stability theorems.- 4. Isolated eigenvalues.- 5. Another form of the stability theorem.- 6. Structure of the spectrum of a closed operator.- § 6. Degenerate perturbations.- 1. The Weinstein-Aronszajn determinants.- 2. The W-A formulas.- 3. Proof of the W-A formulas.- 4. Conditions excluding the singular case.- Five Operators in Hilbert spaces.- § 1. Hilbert space.- 1. Basic notions.- 2. Complete orthonormal families.- § 2. Bounded operators in Hilbert spaces.- 1. Bounded operators and their adjoints.- 2. Unitary and isometric operators.- 3. Compact operators.- 4. The Schmidt class.- 5. Perturbation of orthonormal families.- § 3. Unbounded operators in Hilbert spaces.- 1. General remarks.- 2. The numerical range.- 3. Symmetric operators.- 4. The spectra of symmetric operators.- 5. The resolvents and spectra of selfadjoint operators.- 6. Second-order ordinary differential operators.- 7. The operators T*T.- 8. Normal operators.- 9. Reduction of symmetric operators.- 10. Semibounded and accretive operators.- 11. The square root of an m-accretive operator.- § 4. Perturbation of self adjoint operators.- 1. Stability of selfadjointness.- 2. The case of relative bound 1.- 3. Perturbation of the spectrum.- 4. Semibounded operators.- 5. Completeness of the eigenprojections of slightly non-selfadjoint operators.- § 5. The Schrödinger and Dirac operators.- 1. Partial differential operators.- 2. The Laplacian in the whole space.- 3. The Schrödinger operator with a static potential.- 4. The Dirac operator.- Six Sesquilinear forms in Hilbert spaces and associated operators.- § 1. Sesquilinear and quadratic forms.- 1. Definitions.- 2. Semiboundedness.- 3. Closed forms.- 4. Closable forms.- 5. Forms constructed from sectorial operators.- 6. Sums of forms.- 7. Relative boundedness for forms and operators.- § 2. The representation theorems.- 1. The first representation theorem.- 2. Proof of the first representation theorem.- 3. The Friedrichs extension.- 4. Other examples for the representation theorem.- 5. Supplementary remarks.- 6. The second representation theorem.- 7. The polar decomposition of a closed operator.- § 3. Perturbation of sesquilinear forms and the associated operators.- 1. The real part of an m-sectorial operator.- 2. Perturbation of an m-sectorial operator and its resolvent.- 3. Symmetric unperturbed operators.- 4. Pseudo-Friedrichs extensions.- § 4. Quadratic forms and the Schrödinger operators.- 1. Ordinary differential operators.- 2. The Dirichlet form and the Laplace operator.- 3. The Schrödinger operators in R3.- 4. Bounded regions.- § 5. The spectral theorem and perturbation of spectral families.- 1. Spectral families.- 2. The selfadjoint operator associated with a spectral family.- 3. The spectral theorem.- 4. Stability theorems for the spectral family.- Seven Analytic perturbation theory.- § 1. Analytic families of operators.- 1. Analyticity of vector- and operator-valued functions.- 2. Analyticity of a family of unbounded operators.- 3. Separation of the spectrum and finite systems of eigenvalues.- 4. Remarks on infinite systems of eigenvalues.- 5. Perturbation series.- 6. A holomorphic family related to a degenerate perturbation.- § 2. Holomorphic families of type (A).- 1. Definition.- 2. A criterion for type (A).- 3. Remarks on holomorphic families of type (A).- 4. Convergence radii and error estimates.- 5. Normal unperturbed operators.- § 3. Selfadjoint holomorphic families.- 1. General remarks.- 2. Continuation of the eigenvalues.- 3. The Mathieu, Schrödinger, and Dirac equations.- 4. Growth rate of the eigenvalues.- 5. Total eigenvalues considered simultaneously.- § 4. Holomorphic families of type (B).- 1. Bounded-holomorphic families of sesquilinear forms.- 2. Holomorphic families of forms of type (a) and holomorphic families of operators of type (B).- 3. A criterion for type (B).- 4. Holomorphic families of type (B0).- 5. The relationship between holomorphic families of types (A) and (B).- 6. Perturbation series for eigenvalues and eigenprojections.- 7. Growth rate of eigenvalues and the total system of eigenvalues.- 8. Application to differential operators.- 9. The two-electron problem.- § 5. Further problems of analytic perturbation theory.- 1. Holomorphic families of type (C).- 2. Analytic perturbation of the spectral family.- 3. Analyticity of |H(x)| and |H(x)|?.- § 6. Eigenvalue problems in the generalized form.- 1. General considerations.- 2. Perturbation theory.- 3. Holomorphic families of type (A).- 4. Holomorphic families of type (B).- 5. Boundary perturbation.- Eight Asymptotic perturbation theory.- § 1. Strong convergence in the generalized sense.- 1. Strong convergence of the resolvent.- 2. Generalized strong convergence and spectra.- 3. Perturbation of eigenvalues and eigenvectors.- 4. Stable eigenvalues.- § 2. Asymptotic expansions.- 1. Asymptotic expansion of the resolvent.- 2. Remarks on asymptotic expansions.- 3. Asymptotic expansions of isolated eigenvalues and eigenvectors.- 4. Further asymptotic expansions.- § 3. Generalized strong convergence of sectorial operators.- 1. Convergence of a sequence of bounded forms.- 2. Convergence of sectorial forms “from above”.- 3. Nonincreasing sequences of symmetric forms.- 4. Convergence from below.- 5. Spectra of converging operators.- § 4. Asymptotic expansions for sectorial operators.- 1. The problem. The zeroth approximation for the resolvent.- 2. The 1/2-order approximation for the resolvent.- 3. The first and higher order approximations for the resolvent.- 4. Asymptotic expansions for eigenvalues and eigenvectors.- § 5. Spectral concentration.- 1. Unstable eigenvalues.- 2. Spectral concentration.- 3. Pseudo-eigenvectors and spectral concentration.- 4. Asymptotic expansions.- Nine Perturbation theory for semigroups of operators.- § 1. One-parameter semigroups and groups of operators.- 1. The problem.- 2. Definition of the exponential function.- 3. Properties of the exponential function.- 4. Bounded and quasi-bounded semigroups.- 5. Solution of the inhomogeneous differential equation.- 6. Holomorphic semigroups.- 7. The inhomogeneous differential equation for a holomorphic semigroup.- 8. Applications to the heat and Schrödinger equations.- § 2. Perturbation of semigroups.- 1. Analytic perturbation of quasi-bounded semigroups.- 2. Analytic perturbation of holomorphic semigroups.- 3. Perturbation of contraction semigroups.- 4. Convergence of quasi-bounded semigroups in a restricted sense.- 5. Strong convergence of quasi-bounded semigroups.- 6. Asymptotic perturbation of semigroups.- § 3. Approximation by discrete semigroups.- 1. Discrete semigroups.- 2. Approximation of a continuous semigroup by discrete semigroups.- 3. Approximation theorems.- 4. Variation of the space.- Ten Perturbation of continuous spectra and unitary equivalence.- §1. The continuous spectrum of a selfadjoint operator.- 1. The point and continuous spectra.- 2. The absolutely continuous and singular spectra.- 3. The trace class.- 4. The trace and determinant.- § 2. Perturbation of continuous spectra.- 1. A theorem of Weyl-von Neumann.- 2. A generalization.- § 3. Wave operators and the stability of absolutely continuous spectra.- 1. Introduction.- 2. Generalized wave operators.- 3. A sufficient condition for the existence of the wave operator.- 4. An application to potential scattering.- § 4. Existence and completeness of wave operators.- 1. Perturbations of rank one (special case).- 2. Perturbations of rank one (general case).- 3. Perturbations of the trace class.- 4. Wave operators for functions of operators.- 5. Strengthening of the existence theorems.- 6. Dependence of W± (H2, H1) on H1 and H2.- § 5. A stationary method.- 1. Introduction.- 2. The ? operations.- 3. Equivalence with the time-dependent theory.- 4. The ? operations on degenerate operators.- 5. Solution of the integral equation for rank A = 1.- 6. Solution of the integral equation for a degenerate A.- 7. Application to differential operators.- Supplementary Notes.- Supplementary Bibliography.- Notation index.- Author index.

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Book SynopsisAt the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject. Trade ReviewFrom the reviews:"The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes." (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009)“This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)“The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)Table of ContentsCouplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge—Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.

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Book SynopsisThis, the fourth edition of Stuwe’s book on the calculus of variations, surveys new developments in this exciting field. It also gives a concise introduction to variational methods. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. A number of changes have been made throughout the text.Trade ReviewFrom the reviews of the fourth edition:"The fourth edition of Michael Struwe’s book Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems was published in 2008, 18 years after the first edition. … The bibliography alone would make it a valuable reference as it contains nearly 500 references. … Struwe’s book is addressed to researchers in differential geometry and partial differential equations." (John D. Cook, MAA Online, January, 2009)“This is the fourth edition of a standard reference work on direct methods in the calculus of variations. … The book contains a wealth of important results that would otherwise be hard to find in one single place.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 160 (4), July, 2010)Table of ContentsThe Direct Methods in the Calculus of Variations.- Minimax Methods.- Limit Cases of the Palais-Smale Condition.

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Book SynopsisStochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.Table of ContentsSome elements of stochastic analysis.- Stochastic optimization problems. Examples in finance.- The classical PDE approach to dynamic programming.- The viscosity solutions approach to stochastic control problems.- Optimal switching and free boundary problems.- Backward stochastic differential equations and optimal control.- Martingale and convex duality methods.

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Book SynopsisSince the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.Table of Contents0. Mathematical Preliminaries.- 0.1 Linear Algebra and Linear Programming.- Basic Notation.- Hulls, Independence, Dimension.- Eigenvalues, Positive Definite Matrices.- Vector Norms, Balls.- Matrix Norms.- Some Inequalities.- Polyhedra, Inequality Systems.- Linear (Diophantine) Equations and Inequalities.- Linear Programming and Duality.- 0.2 Graph Theory.- Graphs.- Digraphs.- Walks, Paths, Circuits, Trees.- 1. Complexity, Oracles, and Numerical Computation.- 1.1 Complexity Theory: P and NP.- Problems.- Algorithms and Turing Machines.- Encoding.- Time and Space Complexity.- Decision Problems: The Classes P and NP.- 1.2 Oracles.- The Running Time of Oracle Algorithms.- Transformation and Reduction.- NP-Completeness and Related Notion.- 1.3 Approximation and Computation of Numbers.- Encoding Length of Numbers.- Polynomial and Strongly Polynomial Computations.- Polynomial Time Approximation of Real Numbers.- 1.4 Pivoting and Related Procedures.- Gaussian Elimination.- Gram-Schmidt Orthogonalization.- The Simplex Method.- Computation of the Hermite Normal Form.- 2. Algorithmic Aspects of Convex Sets: Formulation of the Problems.- 2.1 Basic Algorithmic Problems for Convex Sets.- 2.2 Nondeterministic Decision Problems for Convex Sets.- 3. The Ellipsoid Method.- 3.1 Geometric Background and an Informal Description.- Properties of Ellipsoids.- Description of the Basic Ellipsoid Method.- Proofs of Some Lemmas.- Implementation Problems and Polynomiality.- Some Examples.- 3.2 The Central-Cut Ellipsoid Method.- 3.3 The Shallow-Cut Ellipsoid Method.- 4. Algorithms for Convex Bodies.- 4.1 Summary of Results.- 4.2 Optimization from Separation.- 4.3 Optimization from Membership.- 4.4 Equivalence of the Basic Problems.- 4.5 Some Negative Results.- 4.6 Further Algorithmic Problems for Convex Bodies.- 4.7 Operations on Convex Bodies.- The Sum.- The Convex Hull of the Union.- The Intersection.- Polars, Blockers, Antiblockers.- 5. Diophantine Approximation and Basis Reduction.- 5.1 Continued Fractions.- 5.2 Simultaneous Diophantine Approximation: Formulation of the Problems.- 5.3 Basis Reduction in Lattices.- 5.4 More on Lattice Algorithms.- 6. Rational Polyhedra.- 6.1 Optimization over Polyhedra: A Preview.- 6.2 Complexity of Rational Polyhedra.- 6.3 Weak and Strong Problems.- 6.4 Equivalence of Strong Optimization and Separation.- 6.5 Further Problems for Polyhedra.- 6.6 Strongly Polynomial Algorithms.- 6.7 Integer Programming in Bounded Dimension.- 7. Combinatorial Optimization: Some Basic Examples.- 7.1 Flows and Cuts.- 7.2 Arborescences.- 7.3 Matching.- 7.4 Edge Coloring.- 7.5 Matroids.- 7.6 Subset Sums.- 7.7 Concluding Remarks.- 8. Combinatorial Optimization: A Tour d’Horizon.- 8.1 Blocking Hypergraphs and Polyhedra.- 8.2 Problems on Bipartite Graphs.- 8.3 Flows, Paths, Chains, and Cuts.- 8.4 Trees, Branchings, and Rooted and Directed Cuts.- Arborescences and Rooted Cuts.- Trees and Cuts in Undirected Graphs.- Dicuts and Dijoins.- 8.5 Matchings, Odd Cuts, and Generalizations.- Matching.- b-Matching.- T-Joins and T-Cuts.- Chinese Postmen and Traveling Salesmen.- 8.6 Multicommodity Flows.- 9. Stable Sets in Graphs.- 9.1 Odd Circuit Constraints and t-Perfect Graphs.- 9.2 Clique Constraints and Perfect Graphs.- Antiblockers of Hypergraphs.- 9.3 Orthonormal Representations.- 9.4 Coloring Perfect Graphs.- 9.5 More Algorithmic Results on Stable Sets.- 10. Submodular Functions.- 10.1 Submodular Functions and Polymatroids.- 10.2 Algorithms for Polymatroids and Submodular Functions.- Packing Bases of a Matroid.- 10.3 Submodular Functions on Lattice, Intersecting, and Crossing Families.- 10.4 Odd Submodular Function Minimization and Extensions.- References.- Notation Index.- Author Index.

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Book SynopsisThis textbook is an introduction to global optimization, which treats mathematical facts stringently on the one hand, but also motivates them in great detail and illustrates them with 80 figures. The book is therefore not only aimed at mathematicians, but also at natural scientists, engineers and economists who want to understand and apply mathematically sound methods in their field. With almost two hundred pages, the book provides enough choices to use it as a basis for differently designed lectures on global optimization. The detailed treatment of the global solvability of optimization problems under application-relevant conditions sets a new accent that enriches the stock of previous textbooks on optimization. Using the theory and algorithms of smooth convex optimization, the book illustrates that the global solution of a class of optimization problems frequently encountered in practice is efficiently possible, while for the more difficult-to-handle non-convex problems it develops in detail the ideas of branch-and-bound methods.Table of Contents1 Introduction.- 2 Convex optimisation problems.- 3 Non-convex optimisation problems.

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Book SynopsisThis book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.Table of ContentsOptimal stopping: General facts.- Stochastic processes: A brief review.- Optimal stopping and free-boundary problems.- Methods of solution.- Optimal stopping in stochastic analysis.- Optimal stopping in mathematical statistics.- Optimal stopping in mathematical finance.- Optimal stopping in financial engineering.

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Book SynopsisMean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.Table of Contents

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Book Synopsis1. Overview of Optimization Methods in VLSI Design.- 2. High-level Synthesis in VLSI Design.- 3. Optimization Methods in Physical Design.- 4. Power Minimization and Power Grid Synthesis.- 5. Efficient Testing and Verification Methods.- 6. Optimization Approaches for Clocking and Delay Minimization.- 7. VLSI Circuits and Approximate Computing.- 8. Challenges in Full Chip Optimization.

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Book SynopsisTable of ContentsPart 1. MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices (Arrays) 3. Plotting in MATLAB 4. Three-Dimensional Plots 5. Functions 6. Control Flow 7. Miscellaneous Commands and Code Improvement Part 2. Mathematics and MATLAB 8. Transformations and Fern Fractals 9. Complex Numbers and Fractals 10. Series and Taylor Polynomials 11. Numerical Integration 12. The Gram–Schmidt Process Appendices A. Publishing and Live Scripts B. Final Projects C. Linear Algebra Projects D. Multivariable Calculus Projects

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Table of Contents1. Internal stabilization of the phase field system. 2. A solution to the fixed end-point linear quadratic optimal problem. 3. Pattern recognition control systems - a distinct direction in intelligent control. 4. The disturbance attenuation problem for a general class of linear stochastic systems. 5. Conceptual structural elements regarding a speed governor for hydrogenerators. 6. Towards intelligent real-time decision support systems for industrial milieu. 7. Non-analytical approaches to model-based fault detection and isolation. 8. Control of DVD players; focus and tracking control loop. 9. On the structural system analysis in distributed control. 10. On the dynamical control of hyper redundant manipulators. 11. Robots for humanitarian demining. 12. Parametrization of stabilizing controllers with applications. 13. Methodology for the design of feedback active vibration control systems. 14. Future trends in model predictive control. 15. Blocking phenomena analysis for discrete event systems with failures and/or preventive maintenance schedules. 16. Intelligent planning and control in a CIM system. 17. Petri Net Toolbox - teaching discrete event systems under Matlab. 18. Componentwise asymptotic stability - from flow-invariance to Lyapunov functions. 19. Independent component analysis with application to dams displacements monitoring. 20. Fuzzy controllers with dynamics, a systematic design approach. 21. Discrete time linear periodic Hamiltonian systems and applications. 22. Stability of neutral time delay systems: a survey of some results. 23. Slicot-based advanced automatic control computations. 24. On the connection between Riccati inequalities and equations in H8 control problems. 25. New computational approach for the design of fault detection and isolation filters. 26. Setting up the reference input in sliding motion control and its closed-loop tracking performance. 27. Flow-invariance method in control - a survey of some results. 28. ADDENDUM: Brief history of the automatic control degree course at Technical University 'Gh. Asachi' of Iasi.

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Book SynopsisThis volume contains the proceedings of the 200 I International Conference on Operations Research (OR 2(01) held at the Gerhard-Mercator-University Duisburg, September 3-5,2001. OR 200 1 was organized under the auspices of the German Society of Operations Research, Gesellschaft für Operations Research (GOR e. V.). The conference and the annual general meeting were attended by 360 participants from 20 countries. The presentation of 220 papers was organized in 15 sections. According to Duisburg as hosting city for this event OR 200 1 emphasized on contributions of OR in the areas of energy, transport and traftk. The program consisted of2 plenary lectures (Reinhard Selten and Jörg Hennerkes) and 15 invited semiplenary lectures. 97 papers were submitted for publication. Following the advice of the section chairs the program committee decided to accept 59 papers for this volume. The selected manuscripts will be published also in electronic form on the W orld Wide Web at http://www.uni-duisburg.de/or200 1. We want to thank all referees and authors for delivering their final manuscript in due time. We are also grateful to the other members of the local organizing committee and especially to Stefan Krebs, Corinna Schu and David Betge for the perfect conference management. Roland Düsing, Ralph Gollmer and Steffen Stock supported us in editing the abstracts and the final version of this proceeding volume. Last but not least thanks to all the assistants and student assistants for their operations on OR 2001 in Duisburg.Table of ContentsRouting a Fleet of Vehicles for Dynamic Combined Pick-up and Deliveries Services.- Simulating Delays for Realistic Time-Table Optimization.- Was kann Operations Research für die Verkehrstelematik leisten?.- Some Practical Aspects of Periodic Timetabling.- Pickup & Delivery-Probleme mit Umlademöglichkeit. Ein Tourenplanungsproblem aus der Automobilzulieferindustrie.- Zentrale Datenbasis im Energiehandel.- Der Einsatz der Clusteranalyse zur Definition von Referenzanlagen.- MESAP/Times — Advanced Decision Support for Energy and Environmental Planning.- Modellierung und Implementierung von Stammdaten für die Demontageplanung und -Steuerung mit ERP-Systemen.- Energy/Environmental Modeling with the MARKAL Family of Models.- Decision Trees with Parametric Enlarged Local Search.- Acquisition of High-Value Customers for Automotive Banks.- Quantitative Entscheidungsunterstützung für das Preismanagement von TK-Dienstleistungen.- The Estimation of Market Volumes.- Strategies for Capacity Planning in a Complex Production System.- A Simple Queueing Model for the Estimation of Man Machine Interference in Semiconductor Wafer Fabrication.- Optimal Coordination of Manufacturing and Remanufacturing Decisions in Case of Product Substitution.- Planning Sales Territories — A Facility Location Approach.- Eine spieltheoretische Analyse von Zulieferer-Abnehmer-Beziehungen auf Basis des JELS-Modells.- Ein bedingtes Mehrfaktorenmodell zur Quantifizierung der Renditen von Bankaktien auf dem deutschen Kapitalmarkt.- Optimization of European Double-Barrier Options via Optimal Control of the Black-Scholes-Equation.- How to Incorporate Estimation Risk into Markowitz Optimization.- Risk-/Return-orientierte Optimierung des Gesamtbank-Portfolios unter Verwendung des Conditional Value at Risk.- Optimal Properties for Scheduling Deteriorating Jobs for the Total Completion Time Minimization.- Bicriterion Approach to a Single Machine Time-Dependent Scheduling Problem.- Multi-machine Scheduling Problem with Optimal Due Interval Assignment Subject to Generalized Sum Type Criterion.- Storage Problems in Batch Scheduling.- Eine Entscheidung auf Leben und Tod: Decision Support für AIDS-Kontroll-Programme in Ostafrika.- Facilities Layout for Social Institutions.- Slice Models in GAMS.- On Optimal Control of Heating Processes.- On the Relations Between Different Dual Problems in Convex Mathematical Programming.- Total Weighted Completion Time Minimization in a Problem of Scheduling Deteriorating Jobs.- Sensitive Analysis of a Vector Quadratic Lexicographic Boolean Programming Problem.- Some Relations Between Consecutive Ones and Betweenness Polytopes.- Solving One-Dimensional Cutting Stock Problems with Multiple Stock Material Lengths Using Cutting Plane Approach.- Computational Problems that can be Solved Without Computations.- Partitions-requirements-matrices.- On-Line Simulation of Large Scale Networks.- Process-Identification and Optimization of Technical Investments with TEM ?. Bubbles, Quelros and Environmental Management.- Economic Growth, Emission Reduction and the Choice of Energy Technology in a Dynamic-Game Framework.- Measuring Credit Risk: Can we Benefit from Sequential Nonparametric Control?.- Die rationale Marketing-Mix Entscheidung bei vager Kenntnis einzelner Instrumentwirkungen.- Investitionsentscheidungen bei mehrfachen Zielsetzungen und künstliche Ameisen.- Experience-Based Decision Making and Learning from Examples.- Vektoroptimierung bei korrelierten Zielen.- Relevanz von Information in konditionalen Entscheidungsmodellen.- Bestimmung der Gewichte bei Mehrzielentscheidungen. Eine vergleichende Analyse ausgewählter Verfahren.- Wissen ist meßbar.- Constraint Satisfaction by Means of Dynamic Polyhedra.- Multi-Agent FX-Market Modeling by Neural Networks.- Zeitoptimierte Assoziationsanalyse durch Stichprobenauswahl dargestellt am Beispiel aus der Telekommunikationsbranche.- A Metaheuristic-based DSS for Portfolio Optimization.- Kritische Erfolgsfaktoren für die Erstellung universitärer Multimediakurse — mit einem Beispiel aus dem Bereich OR.- Integration von OR-Modellen in die Logistikausbildung: Bearbeitung von Fallbeispielen mit einem Softwarepaket für Studenten.- A Survey of Educational Resources on the Internet.- Internet-based Exercises and Mini-exams for Production and Operations Management.- Mathematische Optimierung zur Unterstützung kundenorientierter Disposition im Schienenverkehr.- Anlagenbelegungsplanung in der Prozeßindustrie.- List of Authors and Coauthors.

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Book SynopsisOmics Data: Acquisition and Mining.- Omics Data: Acquisition and Mining.-  Kernels and Spectrum Perturbations .-  Hadamard Kernel SVM with Applications.-  Regularized Multiple Kernel Learning Framework.-  Correlation Kernels for SVM Classification.- Weighted GTS Kernel and Applications in Drug Side-effect Profiles Prediction.- Single Cell RNA-sequencing Data Analysis.- Kernel Non-negative Matrix Factorization Framework for Single Cell Clustering.- Deep Neural Network with Kernel Nonnegative MatrixFactorization for Single Cell Clustering.-  Multi-omics Single-cell Data Integration via High-order KernelSpectral Clustering.

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Book SynopsisThis is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory.Table of Contents1 Geometry in Regions of a Space. Basic Concepts.- §1. Co-ordinate systems.- 1.1. Cartesian co-ordinates in a space.- 1.2. Co-ordinate changes.- §2. Euclidean space.- 2.1. Curves in Euclidean space.- 2.2. Quadratic forms and vectors.- §3. Riemannian and pseudo-Riemannian spaces.- 3.1. Riemannian metrics.- 3.2. The Minkowski metric.- §4. The simplest groups of transformations of Euclidean space.- 4.1. Groups of transformations of a region.- 4.2. Transformations of the plane.- 4.3. The isometries of 3-dimensional Euclidean space.- 4.4. Further examples of transformation groups.- 4.5. Exercises.- §5. The Serret—Frenet formulae.- 5.1. Curvature of curves in the Euclidean plane.- 5.2. Curves in Euclidean 3-space. Curvature and torsion.- 5.3. Orthogonal transformations depending on a parameter.- 5.4. Exercises.- §6. Pseudo-Euclidean spaces.- 6.1. The simplest concepts of the special theory of relativity.- 6.2. Lorentz transformations.- 6.3. Exercises.- 2 The Theory of Surfaces.- §7. Geometry on a surface in space.- 7.1. Co-ordinates on a surface.- 7.2. Tangent planes.- 7.3. The metric on a surface in Euclidean space.- 7.4. Surface area.- 7.5. Exercises.- §8. The second fundamental form.- 8.1. Curvature of curves on a surface in Euclidean space.- 8.2. Invariants of a pair of quadratic forms.- 8.3. Properties of the second fundamental form.- 8.4. Exercises.- §9. The metric on the sphere.- §10. Space-like surfaces in pseudo-Euclidean space.- 10.1. The pseudo-sphere.- 10.2. Curvature of space-like curves in $$ \mathbb{R}_1^3 $$.- §11. The language of complex numbers in geometry.- 11.1. Complex and real co-ordinates.- 11.2. The Hermitian scalar product.- 11.3. Examples of complex transformation groups.- §12. Analytic functions.- 12.1. Complex notation for the element of length, and for the differential of a function.- 12.2. Complex co-ordinate changes.- 12.3. Surfaces in complex space.- §13. The conformal form of the metric on a surface.- 13.1. Isothermal co-ordinates. Gaussian curvature in terms of conformal co-ordinates.- 13.2. Conformal form of the metrics on the sphere and the Lobachevskian plane.- 13.3. Surfaces of constant curvature.- 13.4. Exercises.- §14. Transformation groups as surfaces in N-dimensional space.- 14.1. Co-ordinates in a neighbourhood of the identity.- 14.2. The exponential function with matrix argument.- 14.3. The quaternions.- 14.4. Exercises.- §15. Conformal transformations of Euclidean and pseudo-Euclidean spaces of several dimensions.- 3 Tensors: The Algebraic Theory.- §16. Examples of tensors.- §17. The general definition of a tensor.- 17.1. The transformation rule for the components of a tensor of arbitrary rank.- 17.2. Algebraic operations on tensors.- 17.3. Exercises.- §18. Tensors of type (0, k).- 18.1. Differential notation for tensors with lower indices only.- 18.2. Skew-symmetric tensors of type (0, k).- 18.3. The exterior product of differential forms. The exterior algebra.- 18.4. Skew-symmetric tensors of type (k, 0) (polyvectors). Integrals with respect to anti-commuting variables.- 18.5. Exercises.- §19. Tensors in Riemannian and pseudo-Riemannian spaces.- 19.1. Raising and lowering indices.- 19.2. The eigenvalues of a quadratic form.- 19.3. The operator ?.- 19.4. Tensors in Euclidean space.- 19.5. Exercises.- §20. The crystallographic groups and the finite subgroups of the rotation group of Euclidean 3-space. Examples of invariant tensors.- §21. Rank 2 tensors in pseudo-Euclidean space, and their eigenvalues.- 21.1. Skew-symmetric tensors. The invariants of an electromagnetic field.- 21.2. Symmetric tensors and their eigenvalues. The energy-momentum tensor of an electromagnetic field.- §22. The behaviour of tensors under mappings.- 22.1. The general operation of restriction of tensors with lower indices.- 22.2. Mappings of tangent spaces.- §23. Vector fields.- 23.1. One-parameter groups of diffeomorphisms.- 23.2. The exponential function of a vector field.- 23.3. The Lie derivative.- 23.4. Exercises.- §24. Lie algebras.- 24.1. Lie algebras and vector fields.- 24.2. The fundamental matrix Lie algebras.- 24.3. Linear vector fields.- 24.4. Left-invariant fields defined on transformation groups.- 24.5. Invariant metrics on a transformation group.- 24.6. The classification of the 3-dimensional Lie algebras.- 24.7. The Lie algebras of the conformal groups.- 24.8. Exercises.- 4 The Differential Calculus of Tensors.- §25. The differential calculus of skew-symmetric tensors.- 25.1. The gradient of a skew-symmetric tensor.- 25.2. The exterior derivative of a form.- 25.3. Exercises.- §26. Skew-symmetric tensors and the theory of integration.- 26.1. Integration of differential forms.- 26.2. Examples of integrals of differential forms.- 26.3. The general Stokes formula. Examples.- 26.4. Proof of the general Stokes formula for the cube.- 26.5. Exercises.- §27. Differential forms on complex spaces.- 27.1. The operators d? and d?.- 27.2. Kählerian metrics. The curvature form.- §28. Covariant differentiation.- 28.1. Euclidean connexions.- 28.2. Covariant differentiation of tensors of arbitrary rank.- §29. Covariant differentiation and the metric.- 29.1. Parallel transport of vector fields.- 29.2. Geodesics.- 29.3. Connexions compatible with the metric.- 29.4. Connexions compatible with a complex structure (Hermitian metric).- 29.5. Exercises.- §30. The curvature tensor.- 30.1. The general curvature tensor.- 30.2. The symmetries of the curvature tensor. The curvature tensor defined by the metric.- 30.3. Examples: The curvature tensor in spaces of dimensions 2 and 3; the curvature tensor of transformation groups.- 30.4. The Peterson—Codazzi equations. Surfaces of constant negative curvature, and the “sine—Gordon” equation.- 30.5. Exercises.- 5 The Elements of the Calculus of Variations.- §31. One-dimensional variational problems.- 31.1. The Euler—Lagrange equations.- 31.2. Basic examples of functional.- §32. Conservation laws.- 32.1. Groups of transformations preserving a given variational problem.- 32.2. Examples. Applications of the conservation laws.- §33. Hamiltonian formalism.- 33.1. Legendre’s transformation.- 33.2. Moving co-ordinate frames.- 33.3. The principles of Maupertuis and Fermat.- 33.4. Exercises.- §34. The geometrical theory of phase space.- 34.1. Gradient systems.- 34.2. The Poisson bracket.- 34.3. Canonical transformations.- 34.4. Exercises.- §35. Lagrange surfaces.- 35.1. Bundles of trajectories and the Hamilton—Jacobi equation.- 35.2. Hamiltonians which are first-order homogeneous with respect to the momentum.- §36. The second variation for the equation of the geodesics.- 36.1. The formula for the second variation.- 36.2. Conjugate points and the minimality condition.- 6 The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants.- §37. The simplest higher-dimensional variational problems.- 37.1. The Euler—Lagrange equations.- 37.2. The energy-momentum tensor.- 37.3. The equations of an electromagnetic field.- 37.4. The equations of a gravitational field.- 37.5. Soap films.- 37.6. Equilibrium equation for a thin plate.- 37.7. Exercises.- §38. Examples of Lagrangians.- §39. The simplest concepts of the general theory of relativity.- §40. The spinor representations of the groups SO(3) and O(3, 1). Dirac’s equation and its properties.- 40.1. Automorphisms of matrix algebras.- 40.2. The spinor representation of the group SO(3).- 40.3. The spinor representation of the Lorentz group.- 40.4. Dirac’s equation.- 40.5. Dirac’s equation in an electromagnetic field. The operation of charge conjugation.- §41. Covariant differentiation of fields with arbitrary symmetry.- 41.1. Gauge transformations. Gauge-invariant Lagrangians.- 41.2. The curvature form.- 41.3. Basic examples.- §42. Examples of gauge-invariant functionals. Maxwell’s equations and the Yang—Mills equation. Functionals with identically zero variational derivative (characteristic classes).

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Book SynopsisThis book addresses the many important problems in service operations management, which can be analyzed using two core methodologies: optimization and queueing theory (including numerical simulation of queues).Trade Review"The book is well written and very easy to follow. The reviewer highly recommends the book to be considered as a textbook for courses on service operations at the senior-undergraduate and graduate levels." (A Journal for the Worldwide Service Science Community, 2011) Table of ContentsPreface. Acknowledgements. 1. Why study services? 1.1 What are services. 1.2 Services as a percent of the economy. 1.3 Public versus private service delivery. 1.4 Why model services? 1.5 Key service decisions. 1.6 Philosophy about models. 1.7 Outline of the book. 1.8 Problems. 1.9 References. METHODOLOGICAL FOUNDATIONS. 2 Optimization. 2.1 Introduction. 2.2 Five key elements of optimization. 2.3 Taxonomy of optimization models. 2.4 You probably have seen one already. 2.5 Linear programming. 2.6 Special network form. 2.7 Integer problems. 2.8 Multiple objective problems. 2.9 Mark’s ten rules of formulating problems. 2.10 Problems. 2.11 References. 3 Queueing theory. 3.1 Introduction. 3.2 What is a queueing theory? 3.3 Key performance metrics for queues and Little’s formula. 3.4 A framework for Markovian queues. 3.5 Key results for non-Markovian queues. 3.6 Solving queueing models numerically. 3.7 When conditions change over time. 3.8 Conclusions. 3.9 Problems. 3.10 References. APPLICATION AREAS. 4 Location and districting problems in services. 4.1 Example applications. 4.2 Taxonomy of location problems. 4.3 Covering problems. 4.4 Median problems - minimizing the demand-weighted average distance. 4.5 Multi-objective models. 4.6 Districting problems. 4.7 Franchise location problems. 4.8 Summary and software. 4.9 Problems. 4.10 References. 5 Inventory decisions in services. 5.1 Why is inventory in a service modeling book? 5.2 EOQ - a basic inventory model. 5.3 Extensions of the EOQ model. 5.4 Time varying demand. 5.5 Uncertain demand and lead times. 5.6 Newsvendor problem and applications. 5.7 Summary. 5.8 Problems. 5.9 References. 6 Resource allocation problems and decisions in services. 6.1 Example resource allocation problems. 6.2 How to formulate an assignment or resource allocation problem. 6.3 Infeasible solutions. 6.4 Assigning students to freshman seminars. 6.5 Assigning students to intersession courses. 6.6 Improving the assignment of zip codes to Congressional districts. 6.7 Summary. 6.8 Problems. 6.9 References. 7 Short-term workforce scheduling. 7.1 Overview of scheduling. 7.2 Simple model. 7.3 Extensions of the simple model. 7.4 More difficult extensions. 7.5 Linking scheduling to service. 7.6 Time-dependent queueing analyzer. 7.7 Assigning specific employees to shifts. 7.8 Summary. 7.9 Problems. 7.10 References. 8 Long-term workforce planning. 8.1 Why is long-term workforce planning an issue? 8.2 Basic model. 8.3 Grouping of skills. 8.4 Planning over time. 8.5 Linking to project scheduling. 8.6 Linking to personnel training and planning in general. 8.7 Simple model of training. 8.8 Summary. 8.9 Problems. 8.10 References. 9 Priority services, call center design and customer scheduling. 9.1 Examples. 9.2 Priority queueing for emergency and other services. service in each class with non-preemptive priorities. 9.2.3 Priority service with Poisson arrivals, multiple servers and identically distributed exponential service times.. 9.2.4 Preemptive queueing. 9.3 Call center design. 9.4 Scheduling in services. 9.5 Summary. 9.6 Problems. 9.7 References. 10 Vehicle routing and services. 10.1 Example routing problems. 10.2 Classification of routing problems. 10.3 Arc routing. 10.4 The traveling salesman problem. 10.5 Vehicle routing problems. 10.6 Summary. 10.7 Problems. 10.8 References. 11 Where to from here? 11.1 Introduction. 11.2 Other methodologies. 11.3 Other applications in services. 11.4 Summary. 11.5 References. APPENDICES. A. Sums of series - basic formulae. B. Overview of probability. B.1. Introduction and basic definitions. B.2 Axioms of probability .. B.3 Joint, marginal and conditional probabilities and Bayes’ theorem. B.4 Counting, ordered pairs, permutations and combinations. B.5 Random variables. B.6 Discrete random variables. B.7 Continuous random variables. B.8 Moment and probability generating functions. B.9 Generating random variables. B.10 Random variables in Excel. C. References.

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Book SynopsisEngineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems.Table of ContentsLinear Spaces. Hilbert Space. Least-Squares Estimation. Dual Spaces. Linear Operators and Adjoints. Optimization of Functionals. Global Theory of Constrained Optimization. Local Theory of Constrained Optimization. Iterative Methods of Optimization. Indexes.

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Book SynopsisAn up-close look at the theory behind and application of extremum seeking Originally developed as a method of adaptive control for hard-to-model systems, extremum seeking solves some of the same problems as today''s neural network techniques, but in a more rigorous and practical way. Following the resurgence in popularity of extremum-seeking control in aerospace and automotive engineering, Real-Time Optimization by Extremum-Seeking Control presents the theoretical foundations and selected applications of this method of real-time optimization. Written by authorities in the field and pioneers in adaptive nonlinear control systems, this book presents both significant theoretic value and important practical potential. Filled with in-depth insight and expert advice, Real-Time Optimization by Extremum-Seeking Control: * Develops optimization theory from the points of dynamic feedback and adaptation * Builds a solid bridge between the classical optimization theory and Trade Review"The subject matter is hard; this short book is therefore presented as an overview." (Computing Reviws.com, March 26, 2004) "…a well-written and authoritative book…an essential resource for learning about extremum-seeking control and for motivating further developments in this subject area." (IEEE Control Systems Magazine, April 2004) “...recommended..” (Choice, Vol. 41, No. 7, March 2004)Table of ContentsPreface ix I Theory 1 II Applications 91 Appendices 199 Bibliography 223 Index 235

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Book SynopsisThis textbook provides a thorough treatment of standard methods such as linear and quadratic programming, Newton-like methods and the conjugate gradient method. The theoretical aspects of the subject include a treatment of optimality conditions and the significance of Lagrange multipliers.Table of ContentsUNCONSTRAINED OPTIMIZATION. Structure of Methods. Newton-like Methods. Conjugate Direction Methods. Restricted Step Methods. Sums of Squares and Nonlinear Equations. CONSTRAINED OPTIMIZATION. Linear Programming. The Theory of Constrained Optimization. Quadratic Programming. General Linearly Constrained Optimization. Nonlinear Programming. Other Optimization Problems. Non-Smooth Optimization. References. Subject Index.

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Book SynopsisA complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms.Table of ContentsProblems and Algorithms. Optimal Trees and Paths. Maximum Flow Problems. Minimum-Cost Flow Problems. Optimal Matchings. Integrality of Polyhedra. The Traveling Salesman Problem. Matroids. NP and NP-Completeness. Appendix. Bibliography. Index.

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Book SynopsisUnique in that it focuses on formulation and case studies rather than solutions procedures covering applications for pure, generalized and integer networks, equivalent formulations plus successful techniques of network models.Table of ContentsNetform Origins and Uses: Why Modeling and Netforms AreImportant. Fundamental Models for Pure Networks. Additional Pure Network Formulation Techniques. Dynamic Network Models. Generalized Networks. Netforms with Discrete Requirements. Appendices. Index.

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Book SynopsisExplores a range of entertaining questions about urban life such as: How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? And, more.Trade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

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Book SynopsisTrade Review"Lane explores secondary, or hidden, mathematical gems that a player might discover upon mature reflection. . . . Just as most car drivers prefer not to inquire how the internal combustion engine works, most video-type users prefer not to ask how computer magic works. For the few who do ask questions, Lane assures us and as his book testifies, 'there's a lot of mathematics under the surface'."---Andrew James Simoson, MathSciNet"Lane explains some pretty technical concepts in an accessible way. . . . A fun survey of interesting maths related through the lens of video games."---Paul Taylor, Aperiodical"The examples [in Power-Up] were carefully chosen from very popular games, so even the most casual player will have heard of the vast majority of the games discussed. In general, Lane's writing is easy to digest, and the use of color and high-quality paper gives the book a nice look and feel." * Choice *"Power­Up is a very readable book based on examples taken from popular video games. . . . It is a pity that too many people are deprived of the pleasure of finding things out via the intellectual game of mathematics. Hopefully, the effort of the likes of Matthew Lane will someday solve the severe marketing problem of mathematics." * Computing Reviews *"Overall the book is excellent. Lane has written a high readable text with colorful illustrations. You won’t regret reading it and maybe Power-Up will add a new level of insight to your computer gaming." * MAA Reviews *"Matthew Lane explores the mathematical underpinning many popular video games in this well-written and very enjoyable book that is pitched at a very broad audience"---Dominic Thorrington, Mathematics TodayTable of ContentsAcknowledgments xi Introduction 1 1. Let's Get Physical 7 1.1 Platforming Perils 7 1.2 Platforming in Three Dimensions 10 1.3 LittleBigPlanet: Exploring Physics through Gameplay 12 1.4 From 2D to 3D: Bending Laws in Portal 14 1.5 Exploring Reality with A Slower Speed of Light 18 1.6 Exploring Alternative Realities 21 1.7 Beyond Physics: Minecraft or Mine Field? 26 1.8 Closing Remarks 27 1.9 Addendum: Describing Distortion 29 2. Repeat Offenders 34 2.1 Let's Play the Feud! 34 2.2 Game Shows and Birthdays 36 2.3 Beyond the First Duplicate 39 2.4 The Draw Something Debacle 41 2.5 Delayed Repetition: Increasing N 46 2.6 Delayed Repetition:Weight Lifting 48 2.7 The Completionist's Dilemma 53 2.8 Closing Remarks 55 2.9 Addendum: In Search of a Minimal k 55 3. Get Out the Voting System 58 3.1 Everybody Votes, but Not for Everything 58 3.2 Plurality Voting: An Example 60 3.3 Ranked-Choice Voting Systems and Arrow's Impossibility Theorem 61 3.4 An Escape from Impossibility? 66 3.5 Is There a "Best" System? 68 3.6 What Game Developers Know that Politicians Don't 71 3.7 The Best of the Rest 76 3.8 Closing Remarks 82 3.9 Addendum: TheWilson Score Confidence Interval 83 4. Knowing the Score 86 4.1 Ranking Players 86 4.2 Orisinal Original 87 4.3 What's in a Score? 91 4.4 Threes! Company 98 4.5 A Mathematical Model of Threes! 100 4.6 Invalid Scores 105 4.7 Lowest of the Low 109 4.8 Highest of the High 116 4.9 Closing Remarks 121 5. The Thrill of the Chase 122 5.1 I'ma GonnaWin! 122 5.2 Shell Games 123 5.3 Green-Shelled Monsters 125 5.4 Generalizations and Limitations 129 5.5 Seeing Red 131 5.6 Apollonius Circle Pursuit 134 5.7 Overview of aWinning Strategy 136 5.8 Pinpointing the Intersections 141 5.9 Blast Radius 145 5.10 The Pursuer and Pursued in Ms. Pac-Man 148 5.11 Concluding Remarks 153 5.12 Addendum: The Pursuit Curve for Red Shells and a Refined Inequality 153 6. Gaming Complexity 158 6.1 From Russia with Fun 158 6.2 P, NP, and Kevin Bacon 160 6.3 Desktop Diversions 165 6.4 Platforming Problems 169 6.5 Fetch Quests: An Overview 170 6.6 Fetch Quests and Traveling Salesmen 175 6.7 Closing Remarks 183 7. The Friendship Realm 184 7.1 Taking It to the Next Level 184 7.2 Friendship as Gameplay: The Sims and Beyond 186 7.3 A Game-Inspired Friendship Model 190 7.4 Approximations to the Model 193 7.5 The Cost of Maintaining a Friendship 195 7.6 From Virtual Friends to Realistic Romance 198 7.7 Modeling Different Personalities 200 7.8 Improving the Model (Again!) 203 7.9 Concluding Remarks 209 8. Order in Chaos 210 8.1 The Essence of Chaos 210 8.2 Love in the Time of Chaos 211 8.3 Shell Games Revisited 216 8.4 How's theWeather? 223 8.5 Concluding Remarks 225 9. The Value of Games 227 9.1 More Important Than Math 227 9.2 Why Games? 230 9.3 What Next? 242 Notes 244 Bibliography 269 Index 273

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Book SynopsisX and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow throughTrade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

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Book SynopsisA collection of some of the work of Frederick J Almgren, Jr, the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. It includes a summary by Sheldon Chang of the famous 1,700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $R^n$.Table of ContentsThe mathematics of F. J. Almgren, Jr. by B. White On Almgren's regularity result by S. X. Chang The homotopy groups of the integral cycle groups by F. J. Almgren, Jr. An isoperimetric inequality by F. J. Almgren, Jr. Three theorems on manifolds with bounded mean curvature by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure by F. J. Almgren, Jr. Measure theoretic geometry and elliptic variational problems by F. J. Almgren, Jr. The structure of limit varifolds associated with minimizing sequences of mappings by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints by F. J. Almgren, Jr. The structure of stationary one dimensional varifolds with positive density by W. K. Allard and F. J. Almgren, Jr. The geometry of soap films and soap bubbles by F. J. Almgren, Jr. and J. E. Taylor Examples of unknotted curves which bound only surfaces of high genus within their convex hulls by F. J. Almgren, Jr. and W. P. Thurston Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals by R. Schoen, L. Simon, and F. J. Almgren, Jr. Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents by F. J. Almgren, Jr. Liquid crystals and geodesics by R. N. Thurston and F. J. Almgren $\mathbf{Q}$ valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two by F. J. Almgren, Jr. Optimal isoperimetric inequalities by F. Almgren Co-area, liquid crystals, and minimal surfaces by F. Almgren, W. Browder, and E. Lieb Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds by F. J. Almgren, Jr. and E. H. Lieb Symmetric decreasing rearrangement is sometimes continuous by F. J. Almgren, Jr. and E. H. Lieb Questions and answers about area-minimizing surfaces and geometric measure theory by F. Almgren Curvature-driven flows: A variational approach by F. Almgren, J. E. Taylor, and L. Wang Questions and answers about geometric evolution processes and crystal growth by F. Almgren.

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Book SynopsisAn Application-Oriented Introduction to Essential Optimization Concepts and Best Practices Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process. Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project. Examples, exercises, and homework throughout reinforce the author's do, not studTable of ContentsContents Preface xix Acknowledgments xxvii Nomenclature xxix About the Companion Website xxxvii Section 1 Introductory Concepts 1 1 Optimization: Introduction and Concepts 3 1.1 Optimization and Terminology 3 1.2 Optimization Concepts and Definitions 4 1.3 Examples 6 1.4 Terminology Continued 10 1.4.1 Constraint 10 1.4.2 Feasible Solutions 10 1.4.3 Minimize or Maximize 11 1.4.4 Canonical Form of the Optimization Statement 11 1.5 Optimization Procedure 12 1.6 Issues That Shape Optimization Procedures 16 1.7 Opposing Trends 17 1.8 Uncertainty 20 1.9 Over- and Under-specification in Linear Equations 21 1.10 Over- and Under-specification in Optimization 22 1.11 Test Functions 23 1.12 Significant Dates in Optimization 23 1.13 Iterative Procedures 26 1.14 Takeaway 27 1.15 Exercises 27 2 Optimization Application Diversity and Complexity 33 2.1 Optimization 33 2.2 Nonlinearity 33 2.3 Min, Max, Min–Max, Max–Min, … 34 2.4 Integers and Other Discretization 35 2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys 36 2.6 Procedures, Not Equations 37 2.7 Static and Dynamic Models 38 2.8 Path Integrals 38 2.9 Economic Optimization and Other Nonadditive Cost Functions 38 2.10 Reliability 39 2.11 Regression 40 2.12 Deterministic and Stochastic 42 2.13 Experimental w.r.t. Modeled OF 43 2.14 Single and Multiple Optima 44 2.15 Saddle Points 45 2.16 Inflections 46 2.17 Continuum and Discontinuous DVs 47 2.18 Continuum and Discontinuous Models 47 2.19 Constraints and Penalty Functions 48 2.20 Ranks and Categorization: Discontinuous OFs 50 2.21 Underspecified OFs 51 2.22 Takeaway 51 2.23 Exercises 51 3 Validation: Knowing That the Answer Is Right 53 3.1 Introduction 53 3.2 Validation 53 3.3 Advice on Becoming Proficient 55 3.4 Takeaway 56 3.5 Exercises 57 Section 2 Univariate Search Techniques 59 4 Univariate (Single DV) Search Techniques 61 4.1 Univariate (Single DV) 61 4.2 Analytical Method of Optimization 62 4.2.1 Issues with the Analytical Approach 63 4.3 Numerical Iterative Procedures 64 4.3.1 Newton’s Methods 64 4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68 4.4 Direct Search Approaches 70 4.4.1 Bisection Method 70 4.4.2 Golden Section Method 72 4.4.3 Perspective at This Point 74 4.4.4 Heuristic Direct Search 74 4.4.5 Leapfrogging 76 4.4.6 LF for Stochastic Functions 79 4.5 Perspectives on Univariate Search Methods 82 4.6 Evaluating Optimizers 85 4.7 Summary of Techniques 85 4.7.1 Analytical Method 86 4.7.2 Newton’s (and Variants Like Secant) 86 4.7.3 Successive Quadratic 86 4.7.4 Golden Section Method 86 4.7.5 Heuristic Direct 87 4.7.6 Leapfrogging 87 4.8 Takeaway 87 4.9 Exercises 88 5 Path Analysis 93 5.1 Introduction 93 5.2 Path Examples 93 5.3 Perspective About Variables 96 5.4 Path Distance Integral 97 5.5 Accumulation along a Path 99 5.6 Slope along a Path 101 5.7 Parametric Path Notation 103 5.8 Takeaway 104 5.9 Exercises 104 6 Stopping and Convergence Criteria: 1-D Applications 107 6.1 Stopping versus Convergence Criteria 107 6.2 Determining Convergence 107 6.2.1 Threshold on the OF 108 6.2.2 Threshold on the Change in the OF 108 6.2.3 Threshold on the Change in the DV 108 6.2.4 Threshold on the Relative Change in the DV 109 6.2.5 Threshold on the Relative Change in the OF 109 6.2.6 Threshold on the Impact of the DV on the OF 109 6.2.7 Convergence Based on Uncertainty Caused by the Givens 109 6.2.8 Multiplayer Range 110 6.2.9 Steady-State Convergence 110 6.3 Combinations of Convergence Criteria 111 6.4 Choosing Convergence Threshold Values 112 6.5 Precision 112 6.6 Other Convergence Criteria 113 6.7 Stopping Criteria to End a Futile Search 113 6.7.1 N Iteration Threshold 114 6.7.2 Execution Error 114 6.7.3 Constraint Violation 114 6.8 Choices! 114 6.9 Takeaway 114 6.10 Exercises 115 Section 3 Multivariate Search Techniques 117 7 Multidimension Application Introduction and the Gradient 119 7.1 Introduction 119 7.2 Illustration of Surface and Terms 122 7.3 Some Surface Analysis 123 7.4 Parametric Notation 128 7.5 Extension to Higher Dimension 130 7.6 Takeaway 131 7.7 Exercises 131 8 Elementary Gradient-Based Optimizers: CSLS and ISD 135 8.1 Introduction 135 8.2 Cauchy’s Sequential Line Search 135 8.2.1 CSLS with Successive Quadratic 137 8.2.2 CSLS with Newton/Secant 138 8.2.3 CSLS with Golden Section 138 8.2.4 CSLS with Leapfrogging 138 8.2.5 CSLS with Heuristic Direct Search 139 8.2.6 CSLS Commentary 139 8.2.7 CSLS Pseudocode 140 8.2.8 VBA Code for a 2-DV Application 141 8.3 Incremental Steepest Descent 144 8.3.1 Pseudocode for the ISD Method 144 8.3.2 Enhanced ISD 145 8.3.3 ISD Code 148 8.4 Takeaway 149 8.5 Exercises 149 9 Second-Order Model-Based Optimizers: SQ and NR 155 9.1 Introduction 155 9.2 Successive Quadratic 155 9.2.1 Multivariable SQ 156 9.2.2 SQ Pseudocode 159 9.3 Newton–Raphson 159 9.3.1 NR Pseudocode 162 9.3.2 Attenuate NR 163 9.3.3 Quasi-Newton 166 9.4 Perspective on CSLS, ISD, SQ, and NR 168 9.5 Choosing Step Size for Numerical Estimate of Derivatives 169 9.6 Takeaway 170 9.7 Exercises 170 10 Gradient-Based Optimizer Solutions: LM, RLM, CG, BFGS, RG, and GRG 173 10.1 Introduction 173 10.2 Levenberg–Marquardt (LM) 173 10.2.1 LM VBA Code for a 2-DV Case 175 10.2.2 Modified LM (RLM) 176 10.2.3 RLM Pseudocode 177 10.2.4 RLM VBA Code for a 2-DV Case 178 10.3 Scaled Variables 180 10.4 Conjugate Gradient (CG) 182 10.5 Broyden–Fletcher–Goldfarb–Shanno (BFGS) 183 10.6 Generalized Reduced Gradient (GRG) 184 10.7 Takeaway 186 10.8 Exercises 186 11 Direct Search Techniques 187 11.1 Introduction 187 11.2 Cyclic Heuristic Direct (CHD) Search 188 11.2.1 CHD Pseudocode 188 11.2.2 CHD VBA Code 189 11.3 Hooke–Jeeves (HJ) 192 11.3.1 HJ Code in VBA 195 11.4 Compare and Contrast CHD and HJ Features: A Summary 197 11.5 Nelder–Mead (NM) Simplex: Spendley, Hext, and Himsworth 199 11.6 Multiplayer Direct Search Algorithms 200 11.7 Leapfrogging 201 11.7.1 Convergence Criteria 208 11.7.2 Stochastic Surfaces 209 11.7.3 Summary 209 11.8 Particle Swarm Optimization 209 11.8.1 Individual Particle Behavior 210 11.8.2 Particle Swarm 213 11.8.3 PSO Equation Analysis 215 11.9 Complex Method (CM) 216 11.10 A Brief Comparison 217 11.11 Takeaway 218 11.12 Exercises 219 12 Linear Programming 223 12.1 Introduction 223 12.2 Visual Representation and Concepts 225 12.3 Basic LP Procedure 228 12.4 Canonical LP Statement 228 12.5 LP Algorithm 229 12.6 Simplex Tableau 230 12.7 Takeaway 231 12.8 Exercises 231 13 Dynamic Programming 233 13.1 Introduction 233 13.2 Conditions 236 13.3 DP Concept 237 13.4 Some Calculation Tips 240 13.5 Takeaway 241 13.6 Exercises 241 14 Genetic Algorithms and Evolutionary Computation 243 14.1 Introduction 243 14.2 GA Procedures 243 14.3 Fitness of Selection 245 14.4 Takeaway 250 14.5 Exercises 250 15 Intuitive Optimization 253 15.1 Introduction 253 15.2 Levels 254 15.3 Takeaway 254 15.4 Exercises 254 16 Surface Analysis II 257 16.1 Introduction 257 16.2 Maximize Is Equivalent to Minimize the Negative 257 16.3 Scaling by a Positive Number Does Not Change DV∗ 258 16.4 Scaled and Translated OFs Do Not Change DV∗ 258 16.5 Monotonic Function Transformation Does Not Change DV∗ 258 16.6 Impact on Search Path or NOFE 261 16.7 Inequality Constraints 263 16.8 Transforming DVs 263 16.9 Takeaway 263 16.10 Exercises 263 17 Convergence Criteria 2: N-D Applications 265 17.1 Introduction 265 17.2 Defining an Iteration 265 17.3 Criteria for Single TS Deterministic Procedures 266 17.4 Criteria for Multiplayer Deterministic Procedures 267 17.5 Stochastic Applications 268 17.7 Takeaway 269 17.8 Exercises 269 18 Enhancements to Optimizers 271 18.1 Introduction 271 18.2 Criteria for Replicate Trials 271 18.3 Quasi-Newton 274 18.4 Coarse–Fine Sequence 275 18.5 Number of Players 275 18.6 Search Range Adjustment 276 18.7 Adjustment of Optimizer Coefficient Values or Options in Process 276 18.8 Initialization Range 277 18.9 OF and DV Transformations 277 18.10 Takeaway 278 18.11 Exercises 278 Section 4 Developing Your Application Statements 279 19 Scaled Variables and Dimensional Consistency 281 19.1 Introduction 281 19.2 A Scaled Variable Approach 283 19.3 Sampling of Issues with Primitive Variables 283 19.4 Linear Scaling Options 285 19.5 Nonlinear Scaling 286 19.6 Takeaway 287 19.7 Exercises 287 20 Economic Optimization 289 20.1 Introduction 289 20.2 Annual Cash Flow 290 20.3 Including Risk as an Annual Expense 291 20.4 Capital 293 20.5 Combining Capital and Nominal Annual Cash Flow 293 20.6 Combining Time Value and Schedule of Capital and Annual Cash Flow 296 20.7 Present Value 297 20.8 Including Uncertainty 298 20.8.1 Uncertainty Models 301 20.8.2 Methods to Include Uncertainty in an Optimization 303 20.9 Takeaway 304 20.10 Exercises 304 21 Multiple OF and Constraint Applications 305 21.1 Introduction 305 21.2 Solution 1: Additive Combinations of the Functions 306 21.2.1 Solution 1a: Classic Weighting Factors 307 21.2.2 Solution 1b: Equal Concern Weighting 307 21.2.3 Solution 1c: Nonlinear Weighting 309 21.3 Solution 2: Nonadditive OF Combinations 311 21.4 Solution 3: Pareto Optimal 311 21.5 Takeaway 316 21.6 Exercises 316 22 Constraints 319 22.1 Introduction 319 22.2 Equality Constraints 320 22.2.1 Explicit Equality Constraints 320 22.2.2 Implicit Equality Constraints 321 22.3 Inequality Constraints 321 22.3.1 Penalty Function: Discontinuous 323 22.3.2 Penalty Function: Soft Constraint 323 22.3.3 Inequality Constraints: Slack and Surplus Variables 325 22.4 Constraints: Pass/Fail Categories 329 22.5 Hard Constraints Can Block Progress 330 22.6 Advice 331 22.7 Constraint-Equivalent Features 332 22.8 Takeaway 332 22.9 Exercises 332 23 Multiple Optima 335 23.1 Introduction 335 23.2 Solution: Multiple Starts 337 23.2.1 A Priori Method 340 23.2.2 A Posteriori Method 342 23.2.3 Snyman and Fatti Criterion A Posteriori Method 345 23.3 Other Options 348 23.4 Takeaway 349 23.5 Exercises 350 24 Stochastic Objective Functions 353 24.1 Introduction 353 24.2 Method Summary for Optimizing Stochastic Functions 356 24.2.1 Step 1: Replicate the Apparent Best Player 356 24.2.2 Step 2: Steady-State Detection 357 24.3 What Value to Report? 358 24.4 Application Examples 359 24.4.1 GMC Control of Hot and Cold Mixing 359 24.4.2 MBC of Hot and Cold Mixing 359 24.4.3 Batch Reaction Management 359 24.4.4 Reservoir and Stochastic Boot Print 361 24.4.5 Optimization Results 362 24.5 Takeaway 365 24.6 Exercises 365 25 Effects of Uncertainty 367 25.1 Introduction 367 25.2 Sources of Error and Uncertainty 368 25.3 Significant Digits 370 25.4 Estimating Uncertainty on Values 371 25.5 Propagating Uncertainty on DV Values 372 25.5.1 Analytical Method 373 25.5.2 Numerical Method 375 25.6 Implicit Relations 378 25.7 Estimating Uncertainty in DV∗ and OF∗ 378 25.8 Takeaway 379 25.9 Exercises 379 26 Optimization of Probable Outcomes and Distribution Characteristics 381 26.1 Introduction 381 26.2 The Concept of Modeling Uncertainty 385 26.3 Stochastic Approach 387 26.4 Takeaway 389 26.5 Exercises 389 27 Discrete and Integer Variables 391 27.1 Introduction 391 27.2 Optimization Solutions 394 27.2.1 Exhaustive Search 394 27.2.2 Branch and Bound 394 27.2.3 Cyclic Heuristic 394 27.2.4 Leapfrogging or Other Multiplayer Search 395 27.3 Convergence 395 27.4 Takeaway 395 27.5 Exercises 395 28 Class Variables 397 28.1 Introduction 397 28.2 The Random Keys Method: Sequence 398 28.3 The Random Keys Method: Dichotomous Variables 400 28.4 Comments 401 28.5 Takeaway 401 28.6 Exercises 401 29 Regression 403 29.1 Introduction 403 29.2 Perspective 404 29.3 Least Squares Regression: Traditional View on Linear Model Parameters 404 29.4 Models Nonlinear in DV 405 29.4.1 Models with a Delay 407 29.5 Maximum Likelihood 408 29.5.1 Akaho’s Method 411 29.6 Convergence Criterion 416 29.7 Model Order or Complexity 421 29.8 Bootstrapping to Reveal Model Uncertainty 425 29.8.1 Interpretation of Bootstrapping Analysis 428 29.8.2 Appropriating Bootstrapping 430 29.9 Perspective 431 29.10 Takeaway 431 29.11 Exercises 432 Section 5 Perspective on Many Topics 441 30 Perspective 443 30.1 Introduction 443 30.2 Classifications 443 30.3 Elements Associated with Optimization 445 30.4 Root Finding Is Not Optimization 446 30.5 Desired Engineering Attributes 446 30.6 Overview of Optimizers and Attributes 447 30.6.1 Gradient Based: Cauchy Sequential Line Search, Incremental Steepest Descent, GRG, Etc. 447 30.6.2 Local Surface Characterization Based: Newton–Raphson, Levenberg–Marquardt, Successive Quadratic, RLM, Quasi-Newton, Etc. 448 30.6.3 Direct Search with Single Trial Solution: Cyclic Heuristic, Hooke–Jeeves, and Nelder–Mead 448 30.6.4 Multiplayer Direct Search Optimizers: Leapfrogging, Particle Swarm, and Genetic Algorithms 448 30.7 Choices 448 30.8 Variable Classifications 449 30.8.1 Nominal 449 30.8.2 Ordinal 450 30.8.3 Cardinal 450 30.9 Constraints 451 30.10 Takeaway 453 30.11 Exercises 453 31 Response Surface Aberrations 459 31.1 Introduction 459 31.2 Cliffs (Vertical Walls) 459 31.3 Sharp Valleys (or Ridges) 459 31.4 Striations 463 31.5 Level Spots (Functions 1, 27, 73, 84) 463 31.6 Hard-to-Find Optimum 466 31.7 Infeasible Calculations 468 31.8 Uniform Minimum 468 31.9 Noise: Stochastic Response 469 31.10 Multiple Optima 471 31.11 Takeaway 473 31.12 Exercises 473 32 Identifying the Models, OF, DV, Convergence Criteria, and Constraints 475 32.1 Introduction 475 32.2 Evaluate the Results 476 32.3 Takeaway 482 32.4 Exercises 482 33 Evaluating Optimizers 489 33.1 Introduction 489 33.2 Challenges to Optimizers 490 33.3 Stakeholders 490 33.4 Metrics of Optimizer Performance 490 33.5 Designing an Experimental Test 492 33.6 Takeaway 495 33.7 Exercises 496 34 Troubleshooting Optimizers 499 34.1 Introduction 499 34.2 DV Values Do Not Change 499 34.3 Multiple DV∗ Values for the Same OF∗ Value 499 34.4 EXE Error 500 34.5 Extreme Values 500 34.6 DV∗ Is Dependent on Convergence Threshold 500 34.7 OF∗ Is Irreproducible 501 34.8 Concern over Results 501 34.9 CDF Features 501 34.10 Parameter Correlation 502 34.11 Multiple Equivalent Solutions 504 34.12 Takeaway 504 34.13 Exercises 504 Section 6 Analysis of Leapfrogging Optimization 505 35 Analysis of Leapfrogging 507 35.1 Introduction 507 35.2 Balance in an Optimizer 508 35.3 Number of Initializations to be Confident That the Best Will Draw All Others to the Global Optimum 510 35.3.1 Methodology 511 35.3.2 Experimental 512 35.3.3 Results 513 35.4 Leap-To Window Amplification Analysis 515 35.5 Analysis of α and M to Prevent Convergence on the Side of a Hill 519 35.6 Analysis of α and M to Minimize NOFE 521 35.7 Probability Distribution of Leap-Overs 522 35.7.1 Data 526 35.8 Takeaway 527 35.9 Exercises 528 Section 7 Case Studies 529 36 Case Study 1: Economic Optimization of a Pipe System 531 36.1 Process and Analysis 531 36.1.1 Deterministic Continuum Model 531 36.1.2 Deterministic Discontinuous Model 534 36.1.3 Stochastic Discontinuous Model 535 36.2 Exercises 536 37 Case Study 2: Queuing Study 539 37.1 The Process and Analysis 539 37.2 Exercises 541 38 Case Study 3: Retirement Study 543 38.1 The Process and Analysis 543 38.2 Exercises 550 39 Case Study 4: A Goddard Rocket Study 551 39.1 The Process and Analysis 551 39.2 Pre-Assignment Note 554 39.3 Exercises 555 40 Case Study 5: Reservoir 557 40.1 The Process and Analysis 557 40.2 Exercises 559 41 Case Study 6: Area Coverage 561 41.1 Description and Analysis 561 41.2 Exercises 562 42 Case Study 7: Approximating Series Solution to an ODE 565 42.1 Concepts and Analysis 565 42.2 Exercises 568 43 Case Study 8: Horizontal Tank Vapor–Liquid Separator 571 43.1 Description and Analysis 571 43.2 Exercises 576 44 Case Study 9: In Vitro Fertilization 579 44.1 Description and Analysis 579 44.2 Exercises 583 45 Case Study 10: Data Reconciliation 585 45.1 Description and Analysis 585 45.2 Exercises 588 Section 8 Appendices 591 Appendix A Mathematical Concepts and Procedures 593 Appendix B Root Finding 605 Appendix C Gaussian Elimination 611 Appendix D Steady-State Identification in Noisy Signals 621 Appendix E Optimization Challenge Problems (2-D and Single OF) 635 Appendix F Brief on VBA Programming: Excel in Office 2013 709 Section 9 References and Index 717 References and Additional Resources 719 Index 723

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Book SynopsisThis book gives a comprehensive account of financial optimization models used to support decision-making for financial engineers. It starts with the classical static mean-variance analysis and portfolio immunization, moves on to scenario-based models, and builds towards multi-period dynamic portfolio optimization.Trade Review“This volume is both a comprehensive guide to optimization techniques useful in financial decision making and a well-illustrated essay on the relationship between theory and practice. While the real problem may always be more complex than any model of it we build, that does not necessarily imply that the largest, most complex model will serve us best. Zenios supplies the reader with a spectrum of optimization models, from simple to complex, and sage advice on how to use them.” From the Foreword by Harry M. Markowitz, Nobel Laureate in Economics “Most books on portfolio optimization focus on continuous time stochastic control models. By contrast, Zenios’s decision to focus on mathematical programming models in financial engineering is an auspicious one. The book is well organized and clearly written, and uses a minimum of technical prerequisites (both mathematical and financial). It should therefore be accessible and of interest to a broad audience: industry practitioners interested in the potential application of optimization to the problems they face, students curious about how optimization is applied in finance, and professional researchers who would like a comprehensive overview of the uses of mathematical programming in financial engineering.” David Saunders, University of WaterlooTable of ContentsForeword: Harry M. Markowitz. Preface. Acknowledgments. Notation. List of Models. I. Introduction. 1. An Optimization View of Financial Engineering. 2. Basics of Risk Management. II. Portfolio Optimization Models. 3. Mean-Variance Analysis. 4. Portfolio Models for Fixed Income. 5. Scenario Optimization. 6. Dynamic Portfolio Optimization with Stochastic Programming. 7. Index Funds. 8. Designing Financial Products. 9. Scenario Generation. III. Applications. 10. International Asset Allocation. 11. Corporate Bond Portfolios. 12. Insurance Policies with Guarantees. 13. Personal Financial Planning. IV. Library of Financial Optimization Models. 14. FINLIB: A Library of Financial Optimization Models. Bibliography. Index

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Book SynopsisThis book gives a comprehensive account of financial optimization models used to support decision-making for financial engineers. It starts with the classical static mean-variance analysis and portfolio immunization, moves on to scenario-based models, and builds towards multi-period dynamic portfolio optimization.Trade Review"This volume is both a comprehensive guide to optimization techniques useful in financial decision making and a well-illustrated essay on the relationship between theory and practice. While the real problem may always be more complex than any model of it we build, that does not necessarily imply that the largest, most complex model will serve us best. Zenios supplies the reader with a spectrum of optimization models, from simple to complex, and sage advice on how to use them."From the Foreword by Harry M. Markowitz, Nobel Laureate in Economics "Most books on portfolio optimization focus on continuous time stochastic control models. By contrast, Zenios's decision to focus on mathematical programming models in financial engineering is an auspicious one. The book is well organized and clearly written, and uses a minimum of technical prerequisites (both mathematical and financial). It should therefore be accessible and of interest to a broad audience: industry practitioners interested in the potential application of optimization to the problems they face, students curious about how optimization is applied in finance, and professional researchers who would like a comprehensive overview of the uses of mathematical programming in financial engineering."David Saunders, University of WaterlooTable of ContentsForeword. Preface. Acknowledgements. List of Models. Notation. I. Introduction. 1. An Optimization View of Financial Engineering. 2. Basics of Risk Management. II. Portfolio Optimization Models. 3. Mean-Variance Analysis. 4. Portfolio Models for Fixed Income. 5. Scenario Optimization. 6. Dynamic Portfolio Optimization with Stochastic Programming. 7. Index Funds. 8. Designing Financial Products. 9. Scenario Generation. III. Applications. 10. Application I: International Asset Allocation. 11. Application II: Corporate Bond Portfolios. 12. Application III: Insurance Policies with Guarantees. 13. Application IV: Personal Financial Planning. IV. Library of Financial Optimization Models. 14. FINLIB: A Library of Financial Optimization Models A. Basics of Optimization. B. Basics of Probability Theory. C. Stochastic Processes. Bibliography. Index.

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Book Synopsis Solve SEO problems using data science. This hands-on book is packed with Python code and data science techniques to help you generate data-driven recommendations and automate the SEO workload. This book is a practical, modern introduction to data science in the SEO context using Python. With social media, mobile, changing search engine algorithms, and ever-increasing expectations of users for super web experiences, too much data is generated for an SEO professional to make sense of in spreadsheets. For any modern-day SEO professional to succeed, it is relevant to find an alternate solution, and data science equips SEOs to grasp the issue at hand and solve it. From machine learning to Natural Language Processing (NLP) techniques, Data-Driven SEO with Python provides tried and tested techniques with full explanations for solving both everyday and complex SEO problems. This book is ideal for SEO professionals who want to take their industry skiTable of ContentsData Driven SEO with PythonChapter 1: Meeting the Challenges of SEO with Data1.1 Agents of change in SEO1.2 The Pillars of SEO Strategy1.3 Installing Python1.4 Using Python for SEOChapter 2: Keyword Research2.1 Data Sources2.2 Google Search Console2.4 Google Trends2.5 Google Suggest2.6 Competitor Analytics2.7 SERPsChapter 3: Technical3.1 Improving CTRs3.2 Allocate keywords to pages based on the copy3.3 Allocating parent nodes to the orphaned URLs3.4 Improve interlinking based on copy3.5 Automate Technical AuditsChapter 4: Content & UX4.1 Content that best satisfies the user query4.2 Splitting and merging URLs4.3 Content Strategy: Planning landing page content Chapter 5: Authority5.1 A little SEO history5.1 The source of authority5.2 Finding good linksChapter 6: Competitors6.1 Defining the problem6.2 Data Strategy6.3 Data Sources6.4 Selecting Your Competitors6.5 Get Features6.6 Explore, Clean and Transform6.7 Modelling The SERPS6.8 Evaluating your Model6.9 ActivationChapter 7: Experiments7.1 How experiments fit into the SEO process7.2 Generating Hypotheses7.3 Experiment Design7.4 Running your experiment7.5 Experiment EvaluationChapter 8: Dashboards8.1 Use a Data Layer8.2 Extract, Transform and Load (ETL)8.3 Transform8.4 Querying the Data Warehouse (DW)8.5 Visualization8.6 Making Future ForecastsChapter 9: Site Migrations and Relaunches9.1 Data sources9.2 Establishing the Impact9.3 Segmenting the URLs9.4 Legacy Site URLs9.5 Priority9.6 RoadmapChapter 10: Google Updates10.1 Data sources10.2 Winners and Losers10.3 Quantifying the Impact10.4 Search Intent10.5 Unique URLs10.6 RecommendationsChapter 11: The Future of SEO11.1 Automation11.2 Your journey to SEO science11.3 Suggest resourcesAppendix: CodeGlossaryIndex

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Book SynopsisOptimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques.In recent years the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications.Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications in a distinct part, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area, followed by chapters detailing applications to a wide range of real-world problems.The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand not only the importance of optimization methods to engineering but also the capabilities of current methods.

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Book SynopsisTensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory – some of which are nontrivial – have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors.Tensor Analysis is unique in that it is the first book on the spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors, which is covered in a chapter.Table of Contents List of Figures. List of Algorithms. Preface. Chapter 1: Introduction. Chapter 2: Eigenvalues of Tensors. Chapter 3: Nonnegative Tensors. Chapter 4: Spectral Hypergraph Theory via Tensors. Chapter 5: Positive Semidefinite Tensors. Chapter 6: Completely Positive Tensors and Copositive Tensors. Bibliography. Index.

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Book SynopsisEngineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements.The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications.Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.Trade ReviewPiecewise affine systems are widely used as modeling and design tools across a number of applications, ranging from robotics to systems biology. These systems require a delicate touch as they can exhibit complex and sometimes surprising features. This impressive book navigates the world of such systems with clarity, technical depth, and elegance.”- Professor Magnus Egerstedt, Georgia Institute of Technology

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Book SynopsisThe mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents: a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century, important connections between the moment problem and many branches of analysis, a unified exposition of important classical results, which are difficult to read in the original journals, and a strong foundation for many areas in modern applied mathematics.

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Book SynopsisOptimization is presented in most multivariable calculus courses as an application of the gradient, and while this treatment makes sense for a calculus course, there is much more to the theory of optimization. Optimization problems are generated constantly, and the theory of optimization has grown and developed in response to the challenges presented by these problems. This textbook aims to show readers how optimization is done in practice and help them to develop an appreciation for the richness of the theory behind the practice.Exercises, problems (including modeling and computational problems), and implementations are incorporated throughout the text to help students learn by doing. Python notes are inserted strategically to help readers complete computational problems and implementations.The Basics of Practical Optimization, Second Edition is intended for undergraduates who have completed multivariable calculus, as well as anyone interested in optimization. The book is appropriate for a course that complements or replaces a standard linear programming course.

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