Optimization Books

Book SynopsisThis book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.Table of Contents1.- Some Elements of Linear-Quadratic Optimal Controls.- 2. Linear-Quadratic Two-Person Differential Games.- 3. Mean-Field Linear-Quadratic Optimal Controls.

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Book SynopsisThe theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry. When unknown or uncertain data in an optimization problem is replaced with parameters, one obtains a multi-parametric optimization problem whose optimal solution comes in the form of a function of the parameters.The theory and methodology presented in this work allows one to solve both Linear Programs and convex Quadratic Programs containing parameters in any location within the problem data as well as multi-objective optimization problems with any number of convex quadratic or linear objectives and linear constraints. Applications of these classes of problems are extremely widespread, ranging from business and economics to chemical and environmental engineering. Prior to this work, no solution procedure existed for these general classes of problems except for the recently proposed algorithmsTable of Contents1. Introduction.- 2. Background on mpLCP.- 3. Algebraic Properties of Invariancy Regions.- 4. Phase 2: Partitioning the Parameter Space.- 5. Phase 1: Determining an Initial Feasible Solution.- 6. Further Considerations.- 7. Assessment of Performance.- 8. Conclusion.- Appendix A. Tableaux for Example 2.1.- Appendix B. Tableaux for Example 2.2.- References.

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Book SynopsisThis brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields.To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.Trade Review“The author successfully presents all of this varied material using a consistent and modern notation. … The book meticulously provides references with a comprehensive list at the end. It includes information about software libraries that implement Riemannian optimization in MATLAB, Python, R, C++, and Julia. Both the proofs and calculations in the examples are given with sufficient detail using a consistent notation.” (Anders Linnér, Mathematical Reviews, October, 2022)“The book is a very nice introductory reference for students, engineers, and practitioners to get started in the field of Riemannian optimization. … A highlight of the book is that it reviews the most important work in the field and also mentions current research topics. Thus, I also highly recommended it to researchers getting a broad overview of what is currently studied in the field, without being too detailed or theoretical.” (Lena Sembach, SIAM Review, Vol. 64 (2), June, 2022)Table of ContentsIntroduction.- Preliminaries and Overview of Euclidean Optimization.- Unconstrained Optimization on Riemannian Manifolds.- Conjugate Gradient Methods on Riemannian Manifolds.- Applications of Riemannian Optimization.- Recent Developments in Riemannian Optimization.

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Book SynopsisThis book introduces readers to Bayesian optimization, highlighting advances in the field and showcasing its successful applications to computer experiments. R code is available as online supplementary material for most included examples, so that readers can better comprehend and reproduce methods. Compact and accessible, the volume is broken down into four chapters. Chapter 1 introduces the reader to the topic of computer experiments; it includes a variety of examples across many industries. Chapter 2 focuses on the task of surrogate model building and contains a mix of several different surrogate models that are used in the computer modeling and machine learning communities. Chapter 3 introduces the core concepts of Bayesian optimization and discusses unconstrained optimization. Chapter 4 moves on to constrained optimization, and showcases some of the most novel methods found in the field. This will be a useful companion to researchers and practitioners working with computer experiments and computer modeling. Additionally, readers with a background in machine learning but minimal background in computer experiments will find this book an interesting case study of the applicability of Bayesian optimization outside the realm of machine learning. Table of Contents1. Computer experiments.- 2. Surrogate models.- 3. Unconstrained optimization.- 4. Constrained optimization.

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Book SynopsisThis book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course. Table of ContentsSequence and Series of Real Numbers.- Limit, Continuity and Differentiability of Functions.- Definite Integral.- Improper Integrals.- Sequence and Series of Functions.- Fourier Series.- References.- Index.

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Book SynopsisEmpowering Sleep Health: Unleashing the Potential of Artificial Intelligence and Data Science in Sleep Disorders.- Polysomnography Raw Data Extraction, Exploration, and Preprocessing.- Sleep stage probabilities derived from neurological or cardio-respiratory signals by means of artificial intelligence.- From Screening at Clinic to Diagnosis at Home: How AI/ ML/DL Algorithms are Transforming Sleep Apnea Detection.- Modeling and Analysis of Mechanical Work of Breathing.- A Probabilistic Perspective: Bayesian Neural Network for Sleep Apnea Detection.- Automatic and machine learning methods for detection and characterization of REM sleep behavior disorder.- Sleep Cyclic Alternating Pattern (CAP) as a Neurophysiological Marker of Brain Health.- Deep Learning with Electrocardiograms.- Machine learning automated analysis applied to mandibular jaw movements during sleep: a window on polysomnography.- Nightmare disorder: An Overview.

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Book SynopsisChapter 1. Artificial Intelligence, Optimization, and Data Sciences in Sports: Editorial.- Chapter 2. Machine Learning for Soccer Match Result Prediction.- Chapter 3. Machine learning for prediction of the index of effec-tiveness in cycling.- Chapter 4. Machine Learning in Biomechanics: Key Applications and Limitations in Walking, Running, and Sports Movements.- Chapter 5. Artificial Intelligence & Machine Learning-Based Data Analytics for Sports. General Overview & NBA Case Study.- Chapter 6. An ecological dynamics approach to the use of Artificial Intelligence and Machine Learning to analyse performance in football.- Chapter 7. A Supervised Learning Approach for Evaluating Football Performances.- Chapter 8. Bridging Route based Cycling Training with Digital Twins.- Chapter 9. Perspectives of Artificial Intelligence in Training and Exercise.- Chapter 10. A fuzzy model for optimise the football rule assuring spectacle, fair play, objectivity and ethics.- Chapter 11. Physical Efficiency in Soccer: Relevance, Correlations and Impacts using AI Methods.- Chapter 12. A PageRank-Based Method for College Football Recruiting Rankings.- Chapter 13. APPLICATIONS OF IMPROVEMENTS TO THE PYTHAGOREAN WON-LOST EXPECTATION IN OPTIMIZING ROSTERS.

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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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