Optimization Books
Cambridge University Press Paradoxes of Belief and Strategic Rationality
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£23.99
Cambridge University Press Approximation Theory and Optimization
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£39.89
Cambridge University Press Infinite Dimensional Optimization and Control Theory 62 Encyclopedia of Mathematics and its Applications Series Number 62
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£98.15
Cambridge University Press Iterative Methods in Combinatorial Optimization 46 Cambridge Texts in Applied Mathematics Series Number 46
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£42.74
Cambridge University Press The Design of Approximation Algorithms
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£56.04
Cambridge University Press Paradoxes of Belief and Strategic Rationality
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£58.00
Cambridge University Press TwoSided Matching A Study in GameTheoretic Modeling and Analysis 18 Econometric Society Monographs
Book SynopsisTwo-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets â The authors are to be warmly congratulated for this fine piece of work, which is quite uniqTrade Review"This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets....The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature." From the Foreword by Robert Aumann"An expertly guided tour through an unfamiliar and beautiful region of equilibrium theory would be quite enough incentive for most economic theorists to buy and read this book. But perhaps the greatest treat offred is Roth's discovery of a happy coincidence between theory and practical affairs." Journal of Economic LiteratureTable of ContentsForeword Robert Auman; Acknowledgment; 1. Introduction; Part I. One-To-One Matching: the Marriage Model: 2. Stable matchings; 3. The structure of the set of stable matchings; 4. Strategic questions; Part II. Many-To-One Matching: Models in which Firms May Employ Many Workers: 5. The college admissions model and the labor market for medical interns; 6. Discrete models with money, and more complex preferences; Part III. Models of One-To-One Matching with Money as a Continuous Variable: 7. A simple model of one seller and many buyers; 8. The assignment game; 9. The generalization of the assignment model; Part IV. Epilogue: 10. Open questions and research directions; Bibliography; Indexes.
£40.84
Cambridge University Press Geometric Control Theory
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£148.20
Cambridge University Press A First Course in Optimization Theory
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£85.49
Cambridge University Press A First Course in Optimization Theory
Book SynopsisThis book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contaTrade Review'… the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, WürzbergTable of Contents1. Mathematical preliminaries; 2. Optimization in Rn; 3. Existence of solutions: the Weierstrass theorem; 4. Unconstrained optima; 5. Equality constraints and the theorem of Lagrange; 6. Inequality constraints and the theorem of Kuhn and Tucker; 7. Convex structures in optimization theory; 8. Quasi-convexity and optimization; 9. Parametric continuity: the maximum theorem; 10. Supermodularity and parametric monotonicity; 11. Finite-horizon dynamic programming; 12. Stationary discounted dynamic programming; Appendix A. Set theory and logic: an introduction; Appendix B. The real line; Appendix C. Structures on vector spaces; Bibliography.
£38.94
Cambridge University Press Graph Algorithms
Book SynopsisShimon Even''s Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.Trade Review'[This book] provides an intensive study of the main topics of the field, with [a] list of problems following each topic and explains algorithms in a formal but simple language with a direct and intuitive presentation. Its usage is not limited to being a textbook for an upper-level undergraduate or a graduate course in mathematics. Thanks to the rich set of results covered it can also be used as a reference book for postgraduate students and researchers in the area of Graph algorithms … Besides being extremely useful to those who are interested in theory of graphs and design of graph algorithms, instructors can also benefit from the easy way it presents various ideas and approaches to problem solutions.' Vladimir Lacko, Zentralblatt MATH'The book is an excellent introduction to (algorithmic) graph theory, and seems to be a good choice for a class on the topic, or for self-study. Each chapter comes with its own selected bibliography, and ends with a collection of problems to help the reader check his or her understanding of the material presented in that chapter. Proofs are always provided and are also the topic of a few selected exercises.' Anthony Labarre, SIGACT NewsTable of Contents1. Paths in graphs; 2. Trees; 3. Depth-first search; 4. Ordered trees; 5. Flow in networks; 6. Applications of network flow techniques; 7. Planar graphs; 8. Testing graph planarity.
£76.95
Cambridge University Press foundationsofcomputationalmathematicsminneapolis2002
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£61.71
Cambridge University Press Compliance Quantified
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£104.50
Cambridge University Press Approximation Theory and Optimization
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£104.50
Cambridge University Press Approaches to the Theory of Optimization
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£35.14
Cambridge University Press Stochastic Control of Partially Observable Systems
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£47.49
Cambridge University Press Graph Algorithms
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£33.24
Cambridge University Press orientedmatroids
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£88.21
Cambridge University Press Optimal Reliability Design Fundamentals and Applications
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£73.80
Cambridge University Press Simplicial Algorithms for Minimizing Polyhedral Functions
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£74.10
Cambridge University Press Estimating Market Power and Strategies
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£104.50
Cambridge University Press A First Course in Combinatorial Optimization 36 Cambridge Texts in Applied Mathematics Series Number 36
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£72.19
Cambridge University Press Boolean Functions
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£147.25
Cambridge University Press Convex Functions Constructions Characterizations and Counterexamples 109 Encyclopedia of Mathematics and its Applications Series Number 109
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£128.25
Cambridge University Press Networks Optimisation and Evolution 21 Cambridge Series in Statistical and Probabilistic Mathematics Series Number 21
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£63.64
Cambridge University Press Mathematical Pictures at a Data Science Exhibition
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£35.14
Cambridge University Press Mathematical Analysis of Machine Learning
Book SynopsisThis self-contained textbook introduces students and researchers of AI to the key mathematical concepts and techniques necessary to learn and analyze machine learning algorithms. Readers will gain the technical knowledge needed to understand research papers in theoretical machine learning, without much difficulty.Trade Review'This graduate-level text gives a thorough, rigorous and up-to-date treatment of the main mathematical tools that have been developed for the analysis and design of machine learning methods. It is ideal for a graduate class, and the exercises at the end of each chapter make it suitable for self-study. An excellent addition to the literature from one of the leading researchers in this area, it is sure to become a classic.' Peter Bartlett, University of California, Berkeley'This book showcases the breadth and depth of mathematical ideas in learning theory. The author has masterfully synthesized techniques from the many disciplines that have contributed to this subject, and presented them in an accessible format that will be appreciated by both newcomers and experts alike. Readers will learn the tools-of-the-trade needed to make sense of the research literature and to express new ideas with clarity and precision.' Daniel Hsu, Columbia University'Tong Zhang shares in this book his deep and broad knowledge of machine learning, writing an impressively comprehensive and up-to-date reference text, providing a rigorous and rather advanced treatment of the most important topics and approaches in the mathematical study of machine learning. As an authoritative reference and introduction, his book will be a great asset to the field.' Robert Schapire, Microsoft Research'This book gives a systematic treatment of the modern mathematical techniques that are commonly used in the design and analysis of machine learning algorithms. Written by a key contributor to the field, it is a unique resource for graduate students and researchers seeking to gain a deep understanding of the theory of machine learning.' Shai Shalev-Shwartz, Hebrew University of JerusalemTable of Contents1. Introduction; 2. Basic probability inequalities for sums of independent random variables; 3. Uniform convergence and generalization analysis; 4. Empirical covering number analysis and symmetrization; 5. Covering number estimates; 6. Rademacher complexity and concentration inequalities; 7. Algorithmic stability analysis; 8. Model selection; 9. Analysis of kernel methods; 10. Additive and sparse models; 11. Analysis of neural networks; 12. Lower bounds and minimax analysis; 13. Probability inequalities for sequential random variables; 14. Basic concepts of online learning; 15. Online aggregation and second order algorithms; 16. Multi-armed bandits; 17. Contextual bandits; 18. Reinforcement learning; A. Basics of convex analysis; B. f-Divergence of probability measures; References; Author index; Subject index.
£42.74
Cambridge University Press Automotive Control Systems
Book SynopsisThis engineering textbook is designed to introduce advanced control systems for vehicles, including advanced automotive concepts and the next generation of vehicles for ITS. For each automotive control problem considered, the authors emphasise the physics and underlying principles behind the control system concept and design.Table of ContentsPreface; Part I. Introduction and Background: 1. Introduction; 2. Automotive control system design process; 3. Review of engine modeling; 4. Review of vehicle dynamics; 5. Human factors and driver modeling; Part II. Powertrain Control Systems: 6. Air-to-fuel ratio control; 7. Control of spark timing; 8. Idle speed control; 9. Transmission control; 10. Control of hybrid vehicles; 11. Modeling and control of fuel cells for vehicles; Part III. Vehicle Control Systems: 12. Cruise and headway control; 13. Antilock brake systems and traction control; 14. Vehicle stability control; 15. Four wheel steering; 16. Active suspensions; Part IV. Intelligent Transportation Systems (ITS): 17. Overview of ITS; 18. Preventing collisions; 19. Automated highway systems (AHS) and platooning; 20. Lateral active safety systems and automated steering; Appendix A. Review of control theory fundamentals; Appendix B. Two-mass three DOF vehicle lateral/yaw/roll model.
£102.00
Cambridge University Press Advanced Aircraft Flight Performance 34 Cambridge Aerospace Series Series Number 34
Book SynopsisThis book discusses aircraft flight performance, focusing on commercial aircraft but also considering examples of high-performance military aircraft. The framework is a multidisciplinary engineering analysis, fully supported by flight simulation, with software validation at several levels. The book covers topics such as geometrical configurations, configuration aerodynamics and determination of aerodynamic derivatives, weight engineering, propulsion systems (gas turbine engines and propellers), aircraft trim, flight envelopes, mission analysis, trajectory optimisation, aircraft noise, noise trajectories and analysis of environmental performance. A unique feature of this book is the discussion and analysis of the environmental performance of the aircraft, focusing on topics such as aircraft noise and carbon dioxide emissions.Trade Review'The book represents a useful reference for practising performance engineers and it would be a good starting point for anyone tasked with carrying out a performance analysis of an aircraft …' The Aeronautical JournalTable of Contents1. Prolegomena; 2. Aircraft models; 3. Weight and balance performance; 4. Aerodynamic performance; 5. Engine performance; 6. Propeller performance; 7. Aeroplane trim; 8. Flight envelopes; 9. Take-off and field performance; 10. Climb performance; 11. Descent and landing performance; 12. Cruise performance; 13. Manoeuvre performance; 14. Thermo-structural performance; 15. Mission analysis; 16. Aircraft noise: noise sources; 17. Aircraft noise: propagation; 18. Aircraft noise: flight trajectories; 19. Environmental performance; 20. Epilogue.
£71.24
Cambridge University Press Chance Strategy and Choice An Introduction to the Mathematics of Games and Elections Cambridge Mathematical Textbooks
Book SynopsisGames and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the SpragueâGrundy theorem and Arrow's impossibility theorem. â Uses an integrative approach to probability, game, and social choice theory â Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies â Contains numerous exercises and examples of varying Trade Review'Sam Smith's book offers an intriguing juxtaposition of chance, strategy, and elections. The mathematical analysis is rigorous without being too formal or forbidding. The applications to topics in economics and political science - including auctions, power, and voting - as well as to parlor games like poker will engage both students and professionals.' Steven Brams, New York University'I like the logical flow and length of the chapters and I like that the layout is simple (no excessively boxed theorems, etc.). There are numerous chapters, with one key concept explained in each. One could envision that each chapter would roughly be covered in a class period.' John Cullinan, Bard College, New York'The author's approach does seem as if it would appeal to a broad range of instructors and students: there are enough chapters that an instructor could choose a collection of topics according to his or her interest. Furthermore, the inclusion of proof-based sections would allow an instructor to use the text for a course targeted at math majors and minors rather than at a general nontechnical audience.' James Parson, Hood College, Maryland'The book is well written and interesting. Students should have little difficulty reading and understanding this book … The book covers the topics with clarity and applies game theory to 'real-world' problems.' Dan Cunningham, State University of New York, Buffalo'While some of Smith's material has origins more than 100 years old, the author engages the reader through modern developments, such as the minimax theorem (1928), the work of John Nash and Kenneth Arrow (1950s) and even more recent developments by Steven Brams, William Zwicker and Alan Taylor (1980s–2000s). The author does an effective job of presenting this material to an audience of non-science majors with no prerequisites. A unique feature of the text is the treatment of combinatorial games such as Nim and Hackenbush alongside traditional two person game theory.' David Vella, Skidmore College, New York'Chance, Strategy, and Choice fits an important niche for general audience textbooks about games, elections, and other introductory material related to social choice theory … One of my favorite features of the book is that it does an excellent job of integrating the topics of games and elections to illustrate the interconnections between the different areas of social choice theory, often through illustrative examples.' Adam Graham-Squire, MAA ReviewsTable of Contents1. Introduction; 2. Games and elections; 3. Chance; 4. Strategy; 5. Choice; 6. Strategy and choice; 7. Choice and chance; 8. Chance and strategy; 9. Nash equilibria; 10. Proofs and counterexamples; 11. Laws of probability; 12. Fairness in elections; 13. Weighted voting; 14. Gambling games; 15. Zero-sum games; 16. Partial conflict games; 17. Take-away games; 18. Fairness and impossibility; 19. Paradoxes and puzzles in probability; 20. Combinatorial games; 21. Borda versus Condorcet; 22. The Sprague–Grundy theorem; 23. Arrow's impossibility theorem.
£34.19
Cambridge University Press Financial Enterprise Risk Management
Book SynopsisAn accessible guide to enterprise risk management for financial institutions, containing all the tools needed to build and maintain an ERM framework. This new expanded edition has been thoroughly updated to reflect new legislation and the creation of the Financial Conduct Authority and the Prudential Regulation Authority.Trade ReviewReview of previous edition: 'Provides all the tools required to build and maintain a comprehensive ERM framework, covering a range of qualitative and quantitative techniques and their uses in identifying, assessing, modelling and measuring risk.' Actuary Magazine'In total, this book provides not only a very comprehensive and accessible introduction to financial enterprise risk management, but also covers advanced topics such as Bayesian networks and current regulatory developments such as Basel III. It clearly demonstrates the importance of risk management for financial institutions and outlines detailed steps and procedures that can be taken to obtain a firm understanding of risk. The book discusses the specific advantages and limitations of current risk management tools and frameworks and provides rich guidance on how to implement ERM on a comprehensive level.' Matthias M. M. Buehlmaier, zbMATHTable of Contents1. An introduction to enterprise risk management; 2. Types of financial institution; 3. Stakeholders; 4. The internal environment; 5. The external environment; 6. Process overview; 7. Definitions of risk; 8. Risk identification; 9. Some useful statistics; 10. Statistical distributions; 11. Modelling techniques; 12. Extreme value theory; 13. Modelling time series; 14. Quantifying particular risks; 15. Risk assessment; 16. Responses to risk; 17. Continuous considerations; 18. Economic capital; 19. Risk frameworks; 20. Case studies; 21. Solutions to questions; References; Index.
£98.80
Cambridge University Press A Gentle Introduction to Optimization
Book SynopsisOptimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.Table of ContentsPreface; 1. Introduction; 2. Solving linear programs; 3. Duality through examples; 4. Duality theory; 5. Applications of duality; 6. Solving integer programs; 7. Nonlinear optimization; Appendix A. Computational complexity; References; Index.
£37.04
John Wiley & Sons Inc Optimal Resource Allocation
Book SynopsisA UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems. Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features: An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology Numerous exercises and case studies from a variety of areas, including communications, transportation, eTable of ContentsPreface xi 1 BASIC MATHEMATICAL REDUNDANCY MODELS 1 1.1 Types of Models 2 1.2 Non-repairable Redundant Group with Active Redundant Units 3 1.3 Non-repairable Redundant Group with Standby Redundant Units 7 1.4 Repairable Redundant Group with Active Redundant Units 10 1.5 Repairable Redundant Group with Standby Redundant Units 13 1.6 Multi-level Systems and System Performance Estimation 15 1.7 Brief Review of Other Types of Redundancy 16 1.8 Time Redundancy 24 1.9 Some Additional Optimization Problems 27 Chronological Bibliography of Main Monographs on Reliability Theory (with topics on Optimization) 30 2 FORMULATION OF OPTIMAL REDUNDANCY PROBLEMS 33 2.1 Problem Description 33 2.2 Formulation of the Optimal Redundancy Problem with a Single Restriction 35 2.3 Formulation of Optimal Redundancy Problems with Multiple Constraints 39 2.4 Formulation of Multi-Criteria Optimal Redundancy Problems 43 Chronological Bibliography 45 3 METHOD OF LAGRANGE MULTIPLIERS 48 Chronological Bibliography 55 4 STEEPEST DESCENT METHOD 56 4.1 The Main Idea of SDM 56 4.2 Description of the Algorithm 57 4.3 The Stopping Rule 60 4.5 Approximate Solution 66 Chronological Bibliography 68 5 DYNAMIC PROGRAMMING 69 5.1 Bellman’s Algorithm 69 5.2 Kettelle’s Algorithm 73 Chronological Bibliography 84 6 UNIVERSAL GENERATING FUNCTIONS 85 6.1 Generating Function 85 6.2 Universal GF (U-function) 87 Chronological Bibliography 94 7 GENETIC ALGORITHMS 96 7.1 Introduction 96 7.2 Structure of Steady-State Genetic Algorithms 100 7.3 Related Techniques 102 Chronological Bibliography 104 8 MONTE CARLO SIMULATION 107 8.1 Introductory Remarks 107 8.2 Formulation of Optimal Redundancy Problems in Statistical Terms 108 8.3 Algorithm for Trajectory Generation 108 8.4 Description of the Idea of the Solution 111 8.5 Inverse Optimization Problem 114 8.6 Direct Optimization Problem 124 Chronological Bibliography 129 9 COMMENTS ON CALCULATION METHODS 130 9.1 Comparison of Methods 130 9.2 Sensitivity Analysis of Optimal Redundancy Solutions 135 10 OPTIMAL REDUNDANCY WITH SEVERAL LIMITING FACTORS 142 10.1 Method of “Weighing Costs” 142 10.2 Method of Generalized Generating Functions 146 Chronological Bibliography 149 11 OPTIMAL REDUNDANCY IN MULTISTATE SYSTEMS 150 Chronological Bibliography 170 12 CASE STUDIES 172 12.1 Spare Supply System for Worldwide Telecommunication System Globalstar 172 12.2 Optimal Capacity Distribution of Telecommunication Backbone Network Resources 179 12.3 Optimal Spare Allocation for Mobile Repair Station 183 Chronological Bibliography 190 13 COUNTER-TERRORISM: PROTECTION RESOURCES ALLOCATION 191 13.1 Introduction 191 13.2 Written Description of the Problem 192 13.3 Evaluation of Expected Loss 195 13.4 Algorithm of Resource Allocation 197 13.5 Branching System Protection 201 13.6 Fictional Case Study 210 13.7 Measures of Defense, Their Effectiveness, and Related Expenses 217 13.8 Antiterrorism Resource Allocation under Fuzzy Subjective Estimates 223 13.9 Conclusion 232 Chronological Bibliography 232 About the author 235
£83.55
ISTE Ltd and John Wiley & Sons Inc Concepts of Combinatorial Optimization, Volume 1
Book SynopsisCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: On the complexity of combinatorial optimization problems, that presents basics about worst-case and randomized complexity; Classical solution methods, that presents the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; Elements from mathematical programming, that presents fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field. Table of ContentsPreface xiii Vangelis Th. PASCHOS PART I. COMPLEXITY OF COMBINATORIAL OPTIMIZATION PROBLEMS 1 Chapter 1. Basic Concepts in Algorithms and Complexity Theory 3 Vangelis Th. PASCHOS 1.1. Algorithmic complexity 3 1.2. Problem complexity 4 1.3. The classes P, NP and NPO 7 1.4. Karp and Turing reductions 9 1.5. NP-completeness 10 1.6. Two examples of NP-complete problems 13 1.7. A few words on strong and weak NP-completeness 16 1.8. A few other well-known complexity classes 17 1.9. Bibliography 18 Chapter 2. Randomized Complexity 21 Jérémy BARBAY 2.1. Deterministic and probabilistic algorithms 22 2.2. Lower bound technique 28 2.3. Elementary intersection problem 35 2.4. Conclusion 37 2.5 Bibliography 37 PART II. CLASSICAL SOLUTION METHODS 39 Chapter 3. Branch-and-Bound Methods 41 Irène CHARON and Olivier HUDRY 3.1. Introduction 41 3.2. Branch-and-bound method principles 43 3.3. A detailed example: the binary knapsack problem 54 3.4. Conclusion 67 3.5. Bibliography 68 Chapter 4. Dynamic Programming 71 Bruno ESCOFFIER and Olivier SPANJAARD 4.1. Introduction 71 4.2. A first example: crossing the bridge 72 4.3. Formalization 75 4.4. Some other examples 79 4.5. Solution 83 4.6. Solution of the examples 88 4.7. A few extensions 90 4.8. Conclusion 98 4.9. Bibliography 98 PART III. ELEMENTS FROM MATHEMATICAL PROGRAMMING 101 Chapter 5. Mixed Integer Linear Programming Models for Combinatorial Optimization Problems 103 Frédérico DELLA CROCE 5.1. Introduction 103 5.2. General modeling techniques 111 5.3. More advanced MILP models 117 5.4. Conclusions 132 5.5. Bibliography 133 Chapter 6. Simplex Algorithms for Linear Programming 135 Frédérico DELLA CROCE and Andrea GROSSO 6.1. Introduction 135 6.2. Primal and dual programs 135 6.3. The primal simplex method 140 6.4. Bland’s rule 145 6.5. Simplex methods for the dual problem 147 6.6. Using reduced costs and pseudo-costs for integer programming 152 6.7. Bibliography 155 Chapter 7. A Survey of some Linear Programming Methods 157 Pierre TOLLA 7.1. Introduction 157 7.2. Dantzig’s simplex method 158 7.3. Duality 162 7.4. Khachiyan’s algorithm 162 7.5. Interior methods 165 7.6. Conclusion 186 7.7. Bibliography 187 Chapter 8. Quadratic Optimization in 0–1 Variables 189 Alain BILLIONNET 8.1. Introduction 189 8.2. Pseudo-Boolean functions and set functions 190 8.3. Formalization using pseudo-Boolean functions 191 8.4. Quadratic pseudo-Boolean functions (qpBf) 192 8.5. Integer optimum and continuous optimum of qpBfs 194 8.6. Derandomization 195 8.7. Posiforms and quadratic posiforms 196 8.8. Optimizing a qpBf: special cases and polynomial cases 198 8.9. Reductions, relaxations, linearizations, bound calculation and persistence 200 8.10. Local optimum 206 8.11. Exact algorithms and heuristic methods for optimizing qpBfs 208 8.12. Approximation algorithms 211 8.13. Optimizing a quadratic pseudo-Boolean function with linear constraints 213 8.14. Linearization, convexification and Lagrangian relaxation for optimizing a qpBf with linear constraints 220 8.15. -Approximation algorithms for optimizing a qpBf with linear constraints 223 8.16. Bibliography 224 Chapter 9. Column Generation in Integer Linear Programming 235 Irène LOISEAU, Alberto CESELLI, Nelson MACULAN and Matteo SALANI 9.1. Introduction 235 9.2. A column generation method for a bounded variable linear programming problem 236 9.3. An inequality to eliminate the generation of a 0–1 column 238 9.4. Formulations for an integer linear program 240 9.5. Solving an integer linear program using column generation 243 9.6. Applications 247 9.7. Bibliography 255 Chapter 10. Polyhedral Approaches 261 Ali Ridha MAHJOUB 10.1. Introduction 261 10.2. Polyhedra, faces and facets 265 10.3. Combinatorial optimization and linear programming 276 10.4. Proof techniques 282 10.5. Integer polyhedra and min–max relations 293 10.6. Cutting-plane method 301 10.7. The maximum cut problem 308 10.8. The survivable network design problem 313 10.9. Conclusion 319 10.10. Bibliography 320 Chapter 11. Constraint Programming 325 Claude LE PAPE 11.1. Introduction 325 11.2. Problem definition 327 11.3. Decision operators 328 11.4. Propagation 330 11.5. Heuristics 333 11.6. Conclusion 336 11.7. Bibliography 336 List of Authors 339 Index 343 Summary of Other Volumes in the Series 347
£150.05
ISTE Ltd and John Wiley & Sons Inc Paradigms of Combinatorial Optimization: Problems
Book SynopsisCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. “Paradigms of Combinatorial Optimization” is divided in two parts: • Paradigmatic Problems, that handles several famous combinatorial optimization problems as max cut, min coloring, optimal satisfiability tsp, etc., the study of which has largely contributed to both the development, the legitimization and the establishment of the Combinatorial Optimization as one of the most active actual scientific domains; • Classical and New Approaches, that presents the several methodological approaches that fertilize and are fertilized by Combinatorial optimization such as: Polynomial Approximation, Online Computation, Robustness, etc., and, more recently, Algorithmic Game Theory.Trade Review"Finally, the essay is useful for researchers and scientists in diverse fields (mathematics, programmers, engineers, etc.) as well as post-graduate students (and even undergraduates)." (Contemporary Physics, 19 August 2011) Table of ContentsPreface xvii Vangelis Th. PASCHOS PART I. PARADIGMATIC PROBLEMS 1 Chapter 1. Optimal Satisfiability 3 Cristina BAZGAN Chapter 2. Scheduling Problems 33 Philippe CHRÉTIENNE and Christophe PICOULEAU Chapter 3. Location Problems 61 Aristotelis GIANNAKOS Chapter 4. MiniMax Algorithms and Games 89 Michel KOSKAS Chapter 5. Two-dimensional Bin Packing Problems 107 Andrea LODI, Silvano MARTELLO, Michele MONACI and Daniele VIGO Chapter 6. The Maximum Cut Problem 131 Walid BEN-AMEUR, Ali Ridha MAHJOUB and José NETO Chapter 7. The Traveling Salesman Problem and its Variations 173 Jérôme MONNOT and Sophie TOULOUSE Chapter 8. 0–1 Knapsack Problems 215 Gérard PLATEAU and Anass NAGIH Chapter 9. Integer Quadratic Knapsack Problems 243 Dominique QUADRI, Eric SOUTIF and Pierre TOLLA Chapter 10. Graph Coloring Problems 265 Dominique DE WERRA and Daniel KOBLER PART II. NEW APPROACHES 311 Chapter 11. Polynomial Approximation 313 Marc DEMANGE and Vangelis Th. PASCHOS Chapter 12. Approximation Preserving Reductions 351 Giorgio AUSIELLO and Vangelis Th. PASCHOS Chapter 13. Inapproximability of Combinatorial Optimization Problems 381 Luca TREVISAN Chapter 14. Local Search: Complexity and Approximation 435 Eric ANGEL, Petros CHRISTOPOULOS and Vassilis ZISSIMOPOULOS Chapter 15. On-line Algorithms 473 Giorgio AUSIELLO and Luca BECCHETTI Chapter 16. Polynomial Approximation for Multicriteria Combinatorial Optimization Problems 511 Eric ANGEL, Evripidis BAMPIS and Laurent GOURVÈS Chapter 17. An Introduction to Inverse Combinatorial Problems 547 Marc DEMANGE and Jérôme MONNOT Chapter 18. Probabilistic Combinatorial Optimization 587 Cécile MURAT and Vangelis Th. PASCHOS Chapter 19. Robust Shortest Path Problems 615 Virginie GABREL and Cécile MURAT Chapter 20. Algorithmic Games 641 Aristotelis GIANNAKOS and Vangelis PASCHOS List of Authors 675 Index 681 Summary of Other Volumes in the Series 689
£294.45
ISTE Ltd and John Wiley & Sons Inc Progress in Combinatorial Optimization: Recent
Book SynopsisThis book presents recent developments and new trends in Combinatorial Optimization. Combinatorial Optimization is an active research area that has applications in many domains such as communications, network design, VLSI, scheduling, production, computational biology. In the past years, new results and major advances have been seen in many areas including computational complexity, approximation algorithms, cutting-plane based methods and submodularity function minimization. More efficient and powerful methods have been developed for approaching real-worlds problems, and new concepts and theoritical results have been introduced.
£223.20
