Optimization Books
Springer International Publishing AG Combinatorial Models for Scheduling Sports
Book SynopsisThis book introduces solutions for sports scheduling problems in a variety of settings. In particular the book covers timetabling, the traveling tournament problem, carryover minimization, breaks minimization, tournament design, tournament planning, and referee assignment. A rich selection of applications to sports such as football, baseball, basketball, cricket or hockey are employed to illustrate the methods and techniques. In a step-by-step tutorial format the book describes the use of graph theory concepts, local search operators and integer programming in the context of sports scheduling. The methods presented in this book are essential to sports scheduling in all its dimensions, from tournaments that are followed by millions of people across the world, with broadcast rights that amount to hundreds of millions of dollars in some competitions, to amateur leagues that require coordination and logistical efforts due to the large number of tournaments and competitors.Table of ContentsLeagues, tournaments, and schedules.- Combinatorial structures.- Metaheuristics and local search.- Integer programming approaches.- Case studies.
£89.99
Springer International Publishing AG Learning and Intelligent Optimization: 17th
Book SynopsisThis book constitutes the refereed proceedings of the 17th International Conference on Learning and Intelligent Optimization, LION-17, held in Nice, France, during June 4–8, 2023.The 40 full papers presented have been carefully reviewed and selected from 83 submissions. They focus on all aspects of unleashing the potential of integrating machine learning and optimization approaches, including automatic heuristic selection, intelligent restart strategies, predict-then-optimize, Bayesian optimization, and learning to optimize.Table of ContentsAnomaly Classification to Enable Self-Healing in Cyber Physical Systems using Process Mining.- Hyper-box Classification Model using Mathematical Programming.- A leak localization algorithm in water distribution networks using probabilistic leak representation and optimal transport distance.- Fast and Robust Constrained Optimization via Evolutionary and Quadratic Programming.- Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing.- A Bayesian optimization algorithm for constrained simulation optimization problems with heteroscedastic noise.- Hierarchical Machine Unlearning.- Explaining the Behavior of Reinforcement Learning Agents using Explaining the Behavior of Reinforcement Learning Agents using.- Deep Randomized Networks for Fast Learning.- Generative models via Optimal Transport and Gaussian Processes.- Real-world streaming process discovery from low-level event data.- Robust Neural Network Approach to System Identification in the High-Noise Regime.- GPU for Monte Carlo Search.- Learning the Bias Weights for Generalized Nested Rollout Policy Adaptation.- Heuristics selection with ML in CP Optimizer.- Model-based feature selection for neural networks: A mixed-integer programming approach.- An Error-Based Measure for Concept Drift Detection and Characterization.- Predict, Tune and Optimize for Data-Driven Shift Scheduling with Uncertain Demands.- On Learning When to Decompose Graphical Models.- Inverse Lighting with Differentiable Physically-Based Model.- Repositioning Fleet Vehicles: a Learning Pipeline.- Bayesian Decision Trees Inspired from Evolutionary Algorithms.- Towards Tackling MaxSAT by Combining Nested Monte Carlo with Local Search.- Relational Graph Attention-based Deep Reinforcement Learning: An Application to Flexible Job Shop Scheduling with Sequence-dependent Setup Times.- Experimental Digital Twin for Job Shops with Transportation Agents.- Learning to Prune Electric Vehicle Routing Problems.- A matheuristic approach for electric bus fleet scheduling.- Class GP: Gaussian Process Modeling for Heterogeneous Functions.- Surrogate Membership for Inferred Metrics in Fairness Evaluation.- The BeMi Stardust: a Structured Ensemble of Binarized Neural Network.- Discovering explicit scale-up criteria in crisis response with decision mining.- Job Shop Scheduling via Deep Reinforcement Learning: a Sequence to Sequence approach.- Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks.- Multi-Task Predict-then-Optimize.- Integrating Hyperparameter Search into Model-Free AutoML with Context-Free Grammars.- Improving subtour elimination constraint generation in Branch-and-Cut algorithms for the TSP with Machine Learning.- Learn, Compare, Search: One Sawmill’s Search for the Best Cutting Patterns Across And/or Trees.- Dynamic Police Patrol Scheduling with Multi-Agent Reinforcement Learning.- Analysis of Heuristics for Vector Scheduling and Vector Bin Packing.- Unleashing the potential of restart by detecting the search stagnation.
£75.99
Springer International Publishing AG Calculus II: Practice Problems, Methods, and
Book SynopsisThis study guide is designed for students taking a Calculus II course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes applications of integration, sequences and series and their applications, polar coordinate systems, and complex numbers. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students’ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based coursesTable of ContentsChapter 1: Problems: Applications of integration.- Chapter 2: Solutions of Problems: Applications of integration.- Chapter 3: Problems: Sequences and series and their applications.- Chapter 4: Solutions of Problems: Sequences and series and their applications.- Chapter 5: Problems: Polar coordinate system.- Chapter 6: Solutions of Problems: Polar coordinate system.- Chapter 7: Problems: Complex numbers.- Chapter 8: Solutions of Problems: Complex numbers.
£40.49
Springer International Publishing AG Functional Analysis, Sobolev Spaces, and Calculus
Book SynopsisThis book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations. In this setting, problems become much more involved and, for this same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the modern calculus of variations and the analytical foundation associated with it. In particular, it covers an extended introduction to basic functional analysis and to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the need for further challenges beyond the topics addressed here will push students to more advanced horizons.Table of Contents1 Motivation and perspective.- Part I: Basic Functional Analysis and Calculus of Variations.- 2 A first exposure to Functional Analysis.- 3 Introduction to convex analysis. The Hahn-Banach and Lax-Milgram theorems.- 4 The Calculus of Variations for one-dimensional problems.- Part II: Basic Operator Theory.- 5 Continuous operators.- 6 Compact operators.- Part III: Multidimensional Sobolev Spaces and Scalar Variational Problems.- 7 Multidimensional Sobolev spaces.- 8 Variational problems.- 9 Finer results in Sobolev spaces and the Calculus of Variations.- Appendix A: Hints and solutions to exercises.- Appendix B: So much to learn.
£49.49
Birkhäuser Variationsrechnung
Book SynopsisEinleitung.- Klassische Theorie in einer Dimension.- Semiklassische Methoden.- Sobolev-Raume.- Vektorwertige Variationsprobleme.- Relaxation.- Konvergenz & Anwendungen.- Anhänge.
£17.09
Birkhauser Verlag AG Basics of Nonlinear Optimization
Book SynopsisThis textbook gives an introduction to optimization tools which arise around the Weierstrass theorem about the minimum of a lower semicontinuous function.
£35.99
Springer Optimization Discrete Mathematics and
Book SynopsisOn the morphism 1 ? 121, 2 ? 12221.- Polynomials and combinatorial identities.- Rainbow Greedy Matching Algorithms.- Predictive models of Non-Performing Loans: the case of Greece.- The Cost of Detection in Interaction Testing.- On the study of cycle chains representing non-reversible Markov chains associated with random walks with jumps in fixed environments.- Applying Distance Measures for Discrete Data.- Demand aggregation and mid-term energy planning problem on the business layer.- Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices.- A Code-based Watermarking Scheme for the Protection of Authenticity of Medical Images.- The minimum cost energy flow problem under demand uncertainty Effect on optimal solution, variability, worst and best case scenarios.- A mathematical study of the Braess's Paradox within a network comprising four nodes, five edges, and linear time functions.- On similiarities between two global optimization algorithms based on different (Bayesian and Lipschitzian) approaches.
£98.99
Springer Biofuel Production Performance and Emission
Book SynopsisPreface.- Introduction to Renewable Energy Resources and Sustainable Feedstocks for Biodiesel.- Studies on oil extraction, biodiesel production methods, and engine performance and emission characteristic.- Experimentation, Modelling, and Analysis of Biodiesel conversion and their engine performance and emission characteristics.- Artificial Intelligence Modelling of engine performance and emission characteristic.- Optimization of engine performance and emission characteristics.
£89.99
Springer International Publishing AG Interval Linear Programming and Extensions
Book Synopsis
£161.99
Springer Variational and PDE Methods in Nonlinear Science
Book Synopsis- 1. Scalar and Vectorial Allen-Cahn Equations and their Asymptotics.- 2. Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling.- 3. Singular Minimizers in Nonlinear Elasticity.
£59.39
De Gruyter Shape optimization and spectral theory
Book Synopsis„Shape optimization and spectral theory” is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar
£124.92
De Gruyter Optimal Control: From Variations to Nanosatellites
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.
£86.45
De Gruyter Differential Equations, Fourier Series, and Hilbert Spaces: Lecture Notes at the University of Siena
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
£60.80
Walter de Gruyter Math Optimization for Artificial Intelligence
Book Synopsis
£122.85
De Gruyter Operational Perspective of Modeling System
Book Synopsis
£139.17
De Gruyter Parametric Optimization and Related Topics
Book Synopsis
£117.50
de Gruyter Multiobjective and Stochastic Optimization Based
Book Synopsis
£134.09
de Gruyter Nichtlineare Diskrete Optimierung
Book Synopsis
£134.09
Springer International Publishing AG Elementary Symplectic Topology and Mechanics
Book SynopsisThis is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.Trade Review“This book brings the reader from the basics of symplectic topology through several concepts and issues relative to Hamiltonian and Lagrangian systems, Hamilton-Jacobi equations, the calculus of variations, and Morse and Lusternik-Schnirelman theories. … The book seems best suited to researchers and students from graduate level onwards.” (Maria Letizia Bertotti, Mathematical Reviews, August, 2015)Table of ContentsBeginning.- Notes on Differential Geometry.- Symplectic Manifolds.- Poisson brackets environment.- Cauchy Problem for H-J equations.- Calculus of Variations and Conjugate Points.- Asymptotic Theory of Oscillating Integrals.- Lusternik-Schnirelman and Morse.- Finite Exact Reductions.- Other instances.- Bibliography.
£47.49
Springer International Publishing AG An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
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.
£41.24
Springer International Publishing AG Convex Optimization in Normed Spaces: Theory, Methods and Examples
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.
£41.24
Springer International Publishing AG Introduction to Uncertainty Quantification
Book SynopsisThis text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study.Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field.T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.Trade Review“Book is one of very few that discuss a vast array of topics in the developing field of uncertainty quantification (UQ). … The text is mathematically rigorous, and though the intended audience is the senior undergraduate or early graduate mathematics student … . this is a book I might recommend to students as a reference for topics related to UQ ... . Overall, this introduction to UQ leaves something to be desired. It is well written … .” (Talea L. Mayo, SIAM Review, Vol. 59 (1), March, 2017)“This book presents a collection of mathematical results related to Uncertainly Quantification (UQ). It is intended as a textbook for senior undergraduate or graduate students with a background in mathematics and statistics. … The book might be suitable for a research seminar where students are exposed for the first time to the mathematics behind UQ.” (Elisabeth Ullmann, Mathematical Reviews, February, 2017)“This book aims to provide an introduction to the mathematics of the quantification of uncertainty. It is intended for students in mathematics and statistics. In the US this would be a graduate level textbook.” (William J. Satzer, MAA Reviews, maa.org, February, 2016)Table of ContentsIntroduction.- Measure and Probability Theory.- Banach and Hilbert Spaces.- Optimization Theory.- Measures of Information and Uncertainty.- Bayesian Inverse Problems.- Filtering and Data Assimilation.- Orthogonal Polynomials and Applications.- Numerical Integration.- Sensitivity Analysis and Model Reduction.- Spectral Expansions.- Stochastic Galerkin Methods.- Non-Intrusive Methods.- Distributional Uncertainty.- References.- Index.
£67.49
Springer International Publishing AG Quality Control with R: An ISO Standards Approach
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
£52.49
Springer International Publishing AG A Guide to Graph Colouring: Algorithms and
Book SynopsisThis book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.Trade Review“The book gives a comprehensive description and handling on arguably one of the most important notions of combinatorics—graph coloring. … The book is nicely written, and carries a big pile of information valuable for both users and researchers in the field.” (András Sándor Pluhár, Mathematical Reviews, February, 2017)“This well-written book will serve as a utilitarian guide to graph coloring and its practical applications. It includes many definitions, theorems, proofs, algorithms, and pointers for further reading. The book will be helpful for teaching courses on graph coloring to students of mathematics and computer science. I strongly recommend it for the intended audience.” (S. V. Nagaraj, Computing Reviews, computingreviews.com, June, 2016)“The book is a comprehensive guide to graph colouring algorithms. … The book is a nice textbook for both undergraduate and graduate students in the areas of operations research and theoretical computer science. … Finally, it is a good source of knowledge for practitioners.” (Marcin Anholcer, zbMATH 1330.05002, 2016)Table of ContentsIntroduction to Graph Colouring.- Bounds and Constructive Algorithms.- Advanced Techniques for Graph Colouring.- Algorithm Case Studies.- Applications and Extensions.- Designing Seating Plans.- Designing Sports Leagues.- Designing University Timetables.- App. A, Computing Resources.- References.- Index.
£79.99
Springer International Publishing AG Convex Analysis and Monotone Operator Theory in
Book SynopsisThis reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated.Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada.Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.Table of Contents
£93.60
Springer International Publishing AG Vector-Valued Partial Differential Equations and Applications: Cetraro, Italy 2013
Book SynopsisCollating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.Table of ContentsPreface.- Bernard Dacorogna: The pullback equation.- Nicola Fusco: The stability of the isoperimetric inequality.- Stefan Müller: Mathematical problems in thin elastic sheets: scaling limits.-packing, crumpling and singularities.- Vladimir Sverák: Aspects of PDEs related to Fluid Flows.
£35.99
Springer International Publishing AG Probabilistic Theory of Mean Field Games with
Book SynopsisThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.Table of ContentsForeword.- Preface to Volume II.- Part I: MFGs with a Common Noise.- Optimization in a Random Environment.- MFGs with a Common Noise: Strong and Weak Solutions.- Solving MFGs with a Common Noise.- Part II: The Master Equation, Convergence, and Approximation Problems.- The Master Field and the Master Equation.- Classical Solutions to the Master Equation.- Convergence and Approximations.- Epilogue to Volume II.- Extensions for Volume II.- References.- Indices.
£100.80
Springer International Publishing AG Optimization and Approximation
Book SynopsisThis book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.Trade Review“This book, consisting of eight chapters, provides an introduction to optimization aimed at engineering and science students. ... This book is equally suitable to those without prior knowledge in the field as well as those already familiar with the key concepts as a useful reference. The book concludes with a very useful appendix containing hints or full solutions to the exercises presented throughout the book.” (Efstratios Rappos, zbMATH 1375.90002, 2018)Table of Contents1 Overview. Part I Mathematical Programming. - 2 Linear Programming.- 3 Nonlinear programming.- 4 Numerical approximation.- Part II Variational problems.- 5 Basic theory for variational problems 6 Numerical approximation of variational problems.- Part III Optimal Control.- 7 Basic facts about optimal control . 8 Numerical approximation of basic optimal control problems, and dynamic programming. Part IV Appendix.- 9 Hints and solutions to exercises.
£49.49
Springer International Publishing AG Geometrical Themes Inspired by the N-body Problem
Book SynopsisPresenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.Table of ContentsPreface.- Complex differential equations and geometric structures (Adolfo Guillot). - Blow-up for the N-body problem. Applications to free homotopy type (Richard Motgomery).- A quick view of Lagrangian Floer homology (Andrés Pedroza).
£23.24
Springer International Publishing AG Partial Differential Equations and Geometric Measure Theory: Cetraro, Italy 2014
Book SynopsisThis book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.Table of ContentsAlberto Farina and Enrico Valdinoci:Introduction.-Alessio Figalli:Global Existence for the Semi-Geostrophic Equations via Sobolev Estimates for Monge-Ampère.-Ireneo Peral Alonso: On Some Elliptic and Parabolic Equations Related to Growth Models.- Enrico Valdinoci: All Functions are (locally) S-harmonic (up to a small error) – and Applications
£52.24
Springer International Publishing AG Convex Analysis and Monotone Operator Theory in
Book SynopsisThis reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated.Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada.Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.Table of Contents
£93.60
Springer International Publishing AG Pyomo — Optimization Modeling in Python
Book SynopsisThis book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. This second edition provides an expanded presentation of Pyomo’s modeling capabilities, providing a broader description of the software that will enable the user to develop and optimize models. Introductory chapters have been revised to extend tutorials; chapters that discuss advanced features now include the new functionalities added to Pyomo since the first edition including generalized disjunctive programming, mathematical programming with equilibrium constraints, and bilevel programming.Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.Trade Review“This book provides a detailed guide to Pyomo for beginners and advanced users from undergraduate students to academic researchers to practitioners. … the book is a good software guide which I strongly recommend to anybody interested in looking for an alternative to commercial modeling languages in general or in learning or intensifying their Pyomo skills in particular.” (Christina Schenk, SIAM Review, Vol. 61 (1), March, 2019)Table of Contents1. Introduction.- Part I. An Introduction to Pyomo.- 2. Mathematical Modeling and Optimization.- 3. Pyomo Overview.- 4. Pyomo Models and Components.- 5. The Pyomo Command.- 6. Data Command Files.- Part II. Advanced Features and Extensions.- 7. Nonlinear Programming with Pyomo.- 8. Structured Modeling with Blocks.- 9. Generalized Disjunctive Programming.- 10. Stochastic Programming Extensions.- 11. Differential Algebraic Equations.- 12. Mathematical Programs with Equilibrium Constraints.- 13. Bilevel Programming.- 14. Scripting.- A. A Brief Python Tutorial.- Index.
£45.99
Springer International Publishing AG Lectures on Convex Optimization
Book SynopsisThis book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.Trade Review“It is a must-read for both students involved in the operations research programs, as well as the researchers in the area of nonlinear programming, in particular in convex optimization.” (Marcin Anholcer, zbMATH 1427.90003, 2020)Table of ContentsIntroduction.- Part I Black-Box Optimization.- 1 Nonlinear Optimization.- 2 Smooth Convex Optimization.- 3 Nonsmooth Convex Optimization.- 4 Second-Order Methods.- Part II Structural Optimization.- 5 Polynomial-time Interior-Point Methods.- 6 Primal-Dual Model of Objective Function.- 7 Optimization in Relative Scale.- Bibliographical Comments.- Appendix A. Solving some Auxiliary Optimization Problems.- References.- Index.
£49.49
Springer International Publishing AG An Introduction to Metaheuristics for
Book SynopsisThe authors stress the relative simplicity, efficiency, flexibility of use, and suitability of various approaches used to solve difficult optimization problems. The authors are experienced, interdisciplinary lecturers and researchers and in their explanations they demonstrate many shared foundational concepts among the key methodologies. This textbook is a suitable introduction for undergraduate and graduate students, researchers, and professionals in computer science, engineering, and logistics.Trade Review“I would recommend this book for students in the area of operations research, but also for students and professionals from other fields (like natural sciences or social sciences) who would like not only to apply metaheuristics to solve the problems … but also to understand how they work.” (Marcin Anholcer, zbMATH 1427.90001, 2020)Table of ContentsProblems, Algorithms, Computational Complexity.- Search Space.- Tabu Search.- Simulated Annealing.- Ant Colony Optimization (ACO).- Non-PSO Optimization.- Firefly Algorithm, Cuckoo Algorithm, Lévy Flights.- Evolutionary Algorithms: Foundations.- Evolutionary Algorithms: Advanced.- Phase Transition in Optimization Problems.- Performance and Limitations of Metaheuristics.- Statistical Analysis of Research Spaces.
£40.49
Springer Fachmedien Wiesbaden Numerische Verfahren der konvexen, nichtglatten
Book SynopsisKonvexe Optimierungsprobleme mit einer nichtglatten Zielfunktion treten in vielen Anwendungen auf, beispielsweise im Zusammenhang mit Penalty-Verfahren für differenzierbare Optimierungsprobleme, mit der Lagrange-Relaxation bei kombinatorischen Optimierungsproblemen oder bei der Strukturoptimierung von Stabwerken. Die wichtigsten numerischen Verfahren zur Lösung solcher Optimierungsprobleme sind Subgradienten- und Bundle-Verfahren. Das Buch gibt eine kompakte Einführung in die Grundlagen dieser Verfahren, die den Leser in die Lage versetzt, einfache Versionen der Verfahren selbst zu implementieren.Table of Contents1 Einführung.- 1.1 Konvexe Mengen und Funktionen.- 1.2 Konvexe Optimierungsaufgaben.- 1.3 Warum spezielle Verfahren?.- 2 Konvexe Mengen und Funktionen.- 2.1 Konvexe Mengen.- 2.2 Projektion auf konvexe Mengen.- 2.3 Trennungssätze.- 2.4 Konvexe Funktionen.- 2.5 Operationen mit konvexen Funktionen.- 2.6 Affine Minoranten.- 2.7 Lokale Lipschitz-Stetigkeit.- 2.8 Subdifferential und Richtungsableitung.- 2.9 Maximumfunktionen.- 3 Konvexe Optimierungsprobleme.- 3.1 Unrestringierte Probleme.- 3.2 Abstiegsrichtungen.- 3.3 Probleme mit allgemeinen konvexen Restriktionen.- 3.4 Lineare Nebenbedingungen.- 4 Das Subgradientenverfahren.- 4.1 Das Verfahren.- 4.2 Konvergenzbetrachtungen.- 4.3 Numerische Beispiele.- 5 Approximative Ableitungen.- 5.1 Approximation des Subdifferentials.- 5.2 Approximation der Richtungsableitung.- 5.3 Approximative Minima.- 5.4 Approximative Abstiegsrichtungen.- 6 Approximative Abstiegsverfahren.- 6.1 Grundlegende Verfahrenskonzepte.- 6.1.1 Verwendung eines Bundles.- 6.1.2 Approximative Suchrichtungen.- 6.1.3 Verfahren mit approximativer Suchrichtung.- 6.2 Das Schrittweitenverfahren.- 6.2.1 Iterative Berechnung der Schrittweite.- 6.2.2 Das Verfahren.- 6.2.3 Konvergenz des Schrittweitenverfahrens.- 6.3 Konstruktion des Bundles.- 6.4 Ein implementierbares Abstiegsverfahren.- 6.4.1 Das Verfahren.- 6.4.2 Konvergenz des Verfahrens.- 7 Bundle-Verfahren.- 7.1 Stopp-Kriterien.- 7.2 Allgemeiner Verfahrensablauf.- 7.3 Numerische Beispiele.- 8 Bundle-Trust-Region-Verfahren.- 8.1 Grundlage des Verfahrens.- 8.2 Das Trust-Region-Problem.- 8.3 Das Verfahrenskonzept.- 8.4 Implementierung des Verfahrens.- 8.4.1 Anpassung des Trust-Region-Parameters.- 8.4.2 Ein Abbruchkriterium.- 8.4.3 Kriterien für einen Abstiegsschritt.- 8.4.4 Kriterien für einen Nullschritt.- 8.4.5 Berechnung des Trust-Region-Parameters.- 8.4.6 Konstruktion des Bundles.- 8.5 Das Bundle-Trust-Region-Verfahren.- 8.6 Konvergenz des Verfahrens.- 8.7 Numerische Beispiele.- 8.8 Probleme mit linearen Restriktionen.- Übungsaufgaben.
£26.59
Springer Fachmedien Wiesbaden Numerik der Optimierung
Book Synopsis1 Optimierungsaufgaben und Optimalitätskriterien.- 1.1 Globale und lokale Optima, Konvexität.- 1.2 Optimalitätsbedingungen.- 1.3 Semiinfinite Probleme.- 1.4 Ganzzahlige Probleme.- 1.5 Optimierung über Graphen.- 2 Dualität.- 2.1 Duale Probleme.- 2.2 Gestörte Optimierungsprobleme.- 2.3 Anwendungen der Dualität.- 3 Minimierung ohne Restriktionen.- 3.1 Gradientenverfahren.- 3.2 Das Newton-Verfahren.- 3.3 Quasi-Newton-Verfahren.- 3.4 CG-Verfahren.- 3.5 Minimierung nichtglatter Funktionen.- 4 Linear restringierte Probleme.- 4.1 Polyedrische Mengen.- 4.2 Lineare Optimierung.- 4.3 Minimierung über Mannigfaltigkeiten.- 4.4 Probleme mit Ungleichungsrestriktionen.- 5 Strafmethoden.- 5.1 Das Grundprinzip von Strafmethoden.- 5.2 Konvergenzabschätzungen.- 5.3 Modifizierte Lagrange-Funktionen.- 5.4 Strafmethoden und elliptische Randwertprobleme.- 6 Approximationsverfahren.- 6.1 Verfahren der zulässigen Richtungen.- 6.2 Überlinear konvergente Verfahren.- 7 Komplexität.- 7.1 Definitionen, Polynomialität.- 7.2 Nichtdeterministisch polynomiale Algorithmen.- 7.3 Optimierungsprobleme und die Klasse NP-hart.- 7.4 Komplexität in der linearen Optimierung.- 8 Innere-Punkt-Methoden.- 8.1 Innerer-Pfad-Methode für lineare Probleme.- 8.2 Parameterfreies Potential.- 8.3 Der Algorithmus von Karmarkar.- 8.4 Komplementaritätsprobleme.- 8.5 Komplexität der linearen Optimierung.- 9 Aufgaben über Graphen.- 9.1 Definitionen.- 9.2 Graphen und lineare Optimierung.- 9.3 Aufdatierungen in Graphen.- 9.4 Probleme aus der Klasse NP-vollständig.- 10 Die Methode branch and bound.- 10.1 Relaxation, Separation, Strategien.- 10.2 Branch and bound für GLO.- 10.3 Das Rundreiseproblem.- 11 Dekomposition.- 11.1 Dekompositionsprinzipien.- 11.2 Dynamische Optimierung.- 11.3 Ausgewählte Anwendungen.- 12Strukturuntersuchungen.- 12.1 Ganzzahlige Polyeder.- 12.2 Gültige Ungleichungen.- 12.3 Matroide, Greedy-Algorithmus.Table of ContentsAufgabenstellung und Optimalitätskriterien - Dualität, Minimierung ohne Restriktionen - Optimierungsverfahren für linear restringierte Probleme - Penalty-Verfahren und modifizierte Lagrange-Methoden - Verfahren auf der Basis lokaler Approximationen - Komplexität - Innere-Punkt-Methoden - Graphentheoretische Modelle und Verfahren - Die Methode branch and bound - Dekompositionstechniken für strukturierte Optimierungsprobleme - Strukturuntersuchungen in ganzzahligen Optimierungsproblemen
£26.59
Springer Fachmedien Wiesbaden Grundlagen der Mathematischen Optimierung:
Book SynopsisDas Buch stellt wesentliche Ansätze, Ergebnisse und Methoden der linearen und ganzzahligen Optimierung dar. Ziel ist es, eine solide mathematische Grundlage des Gebietes und seiner wichtigsten algorithmischen Ansätze zu entwickeln. Methodisch zentral ist der geometrische Zugang.Table of ContentsEinleitung. - Einstiege: Ungleichungssysteme und diskrete Strukturen. - Einstiege: Algorithmen und Komplexität. - Konvexitätstheorie - Der Simplex-Algorithmus. - LP-Dualität.
£32.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Operations Research Proceedings 2002: Selected
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.
£123.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Operations Research Proceedings 2001: Selected
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.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Perturbation Theory for Linear Operators
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.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Optimal Transport: Old and New
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.
£113.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
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.
£113.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Convex Analysis and Minimization Algorithms II:
Book SynopsisFrom the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"Trade ReviewFrom the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books. . . [is] that they are designed not for the expert, but for those who wish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"Table of ContentsIX. Inner Construction of the Subdifferential.- X. Conjugacy in Convex Analysis.- XI. Approximate Subdifferentials of Convex Functions.- XII. Abstract Duality for Practitioners.- XIII. Methods of ?-Descent.- XIV. Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods.- XV. Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods.- Bibliographical Comments.- References.
£82.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Continuous-time Stochastic Control and
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.
£56.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Geometric Algorithms and Combinatorial Optimization
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.
£104.49
Springer Fachmedien Wiesbaden Mathematische Optimierung: Eine Einführung in die
Book SynopsisDas essential gibt Bachelor- und Masterstudierenden der Ingenieur- und Naturwissenschaften sowie der Wirtschaftswissenschaften eine kurze, anschauliche Einführung in die mathematische Optimierung. Anhand zahlreicher Beispiele werden die Grundbegriffe und Kernaussagen der kontinuierlichen Optimierung erläutert und angewendet. Es werden sowohl Optimierungsprobleme mit und ohne Nebenbedingungen als auch mehrkriterielle Probleme mit mehr als einer Zielfunktion behandelt.Table of ContentsBeispielprobleme: Ausgleichskurve, Standortplanung, Haltestellenproblem.- Optimalitätskriterien erster und zweiter Ordnung.- Karush-Kuhn-Tucker-Bedingungen, Pareto-optimale Lösungen und Pareto-Menge.- Methode der gewichteten Summe.
£9.99
Springer Fachmedien Wiesbaden Algorithm-Driven Truss Topology Optimization for Additive Manufacturing
Book SynopsisSince Additive Manufacturing (AM) techniques allow the manufacture of complex-shaped structures the combination of lightweight construction, topology optimization, and AM is of significant interest. Besides the established continuum topology optimization methods, less attention is paid to algorithm-driven optimization based on linear optimization, which can also be used for topology optimization of truss-like structures.To overcome this shortcoming, we combined linear optimization, Computer-Aided Design (CAD), numerical shape optimization, and numerical simulation into an algorithm-driven product design process for additively manufactured truss-like structures. With our Ansys SpaceClaim add-in construcTOR, which is capable of obtaining ready-for-machine-interpretation CAD data of truss-like structures out of raw mathematical optimization data, the high performance of (heuristic-based) optimization algorithms implemented in linear programming software is now available to the CAD community.Table of ContentsIntroduction.- Physical and Technical Background.- Optimization of Truss Structures.- Bridging Algorithm-Driven Truss Optimization and Additive Manufacturing.- Mixed-Integer Linear Programming for Truss Optimization.- CAD-Based Mathematical Optimization.- Computational Study.- Conclusion and Outlook.
£62.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Basic Concepts of Global Optimization
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.
£44.99
