Linear programming Books

Book SynopsisThe authoritative guide to modeling and solving complex problems with linear programmingextensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics. The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the Fourth Edition<Trade Review"The book can be used both as reference and as textbook for advanced undergraduate students and first-year graduate students in the fields of industrial engineering, management, operation research, computer science, mathematics and other engineering disciplines that deal with the subjects of linear programming and network flows." (Zentralblatt MATH, 2011) Table of ContentsPreface. ONE: INTRODUCTION. 1.1 The Linear Programming Problem. 1.2 Linear Programming Modeling and Examples. 1.3 Geometric Solution. 1.4 The Requirement Space. 1.5 Notation. Exercises. Notes and References. TWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND POLYHEDRAL SETS. 2.1 Vectors. 2.2 Matrices. 2.3 Simultaneous Linear Equations. 2.4 Convex Sets and Convex Functions. 2.5 Polyhedral Sets and Polyhedral Cones. 2.6 Extreme Points, Faces, Directions, and Extreme Directions of Polyhedral Sets: Geometric Insights. 2.7 Representation of Polyhedral Sets. Exercises. Notes and References. THREE: THE SIMPLEX METHOD. 3.1 Extreme Points and Optimality. 3.2 Basic Feasible Solutions. 3.3 Key to the Simplex Method. 3.4 Geometric Motivation of the Simplex Method. 3.5 Algebra of the Simplex Method. 3.6 Termination: Optimality and Unboundedness. 3.7 The Simplex Method. 3.8 The Simplex Method in Tableau Format. 3.9 Block Pivoting. Exercises. Notes and References. FOUR: STARTING SOLUTION AND CONVERGENCE. 4.1 The Initial Basic Feasible Solution. 4.2 The Two-Phase Method. 4.3 The Big-M Method. 4.4 How Big Should Big-M Be? 4.5 The Single Artificial Variable Technique. 4.6 Degeneracy, Cycling, and Stalling. 4.7 Validation of Cycling Prevention Rules. Exercises. Notes and References. FIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND OPTIMALITY CONDITIONS. 5.1 The Revised Simplex Method. 5.2 The Simplex Method for Bounded Variables. 5.3 Farkas’ Lemma via the Simplex Method. 5.4 The Karush-Kuhn-Tucker Optimality Conditions. Exercises. Notes and References. SIX: DUALITY AND SENSITIVITY ANALYSIS. 6.1 Formulation of the Dual Problem. 6.2 Primal-Dual Relationships. 6.3 Economic Interpretation of the Dual. 6.4 The Dual Simplex Method. 6.5 The Primal-Dual Method. 6.6 Finding an Initial Dual Feasible Solution: The Artificial Constraint Technique. 6.7 Sensitivity Analysis. 6.8 Parametric Analysis. Exercises. Notes and References. SEVEN: THE DECOMPOSITION PRINCIPLE. 7.1 The Decomposition Algorithm. 7.2 Numerical Example. 7.3 Getting Started. 7.4 The Case of Unbounded Region X. 7.5 Block Diagonal or Angular Structure. 7.6 Duality and Relationships with other Decomposition Procedures. Exercises. Notes and References. EIGHT: COMPLEXITY OF THE SIMPLEX ALGORITHM AND POLYNOMIAL-TIME ALGORITHMS. 8.1 Polynomial Complexity Issues. 8.2 Computational Complexity of the Simplex Algorithm. 8.3 Khachian’s Ellipsoid Algorithm. 8.4 Karmarkar’s Projective Algorithm. 8.5 Analysis of Karmarkar’s Algorithm: Convergence, Complexity, Sliding Objective Method, and Basic Optimal Solutions. 8.6 Affine Scaling, Primal-Dual Path-Following, and Predictor-Corrector Variants of Interior Point Methods. Exercises. Notes and References. NINE: MINIMAL-COST NETWORK FLOWS. 9.1 The Minimal-Cost Network Flow Problem. 9.2 Some Basic Definitions and Terminology from Graph Theory. 9.3 Properties of the A Matrix. 9.4 Representation of a Nonbasic Vector in Terms of the Basic Vectors. 9.5 The Simplex Method for Network Flow Problems. 9.6 An Example of the Network Simplex Method. 9.7 Finding an Initial Basic Feasible Solution. 9.8 Network Flows with Lower and Upper Bounds. 9.9 The Simplex Tableau Associated with a Network Flow Problem. 9.10 List Structures for Implementing the Network Simplex Algorithm. 9.11 Degeneracy, Cycling, and Stalling. 9.12 Generalized Network Problems. Exercises. Notes and References. TEN: THE TRANSPORTATION AND ASSIGNMENT PROBLEMS. 10.1 Definition of the Transportation Problem. 10.2 Properties of the A Matrix. 10.3 Representation of a Nonbasic Vector in Terms of the Basic Vectors. 10.4 The Simplex Method for Transportation Problems. 10.5 Illustrative Examples and a Note on Degeneracy. 10.6 The Simplex Tableau Associated with a Transportation Tableau. 10.7 The Assignment Problem: (Kuhn’s) Hungarian Algorithm. 10.8 Alternating Path Basis Algorithm for Assignment Problems. 10.9 A Polynomial-Time Successive Shortest Path Approach for Assignment Problems. 10.10 The Transshipment Problem. Exercises. Notes and References. ELEVEN: THE OUT-OF-KILTER ALGORITHM. 11.1 The Out-of-Kilter Formulation of a Minimal Cost Network Flow Problem. 11.2 Strategy of the Out-of-Kilter Algorithm. 11.3 Summary of the Out-of-Kilter Algorithm. 11.4 An Example of the Out-of-Kilter Algorithm. 11.5 A Labeling Procedure for the Out-of-Kilter Algorithm. 11.6 Insight into Changes in Primal and Dual Function Values. 11.7 Relaxation Algorithms. Exercises. Notes and References. TWELVE: MAXIMAL FLOW, SHORTEST PATH, MULTICOMMODITY FLOW, AND NETWORK SYNTHESIS PROBLEMS. 12.1 The Maximal Flow Problem. 12.2 The Shortest Path Problem. 12.3 Polynomial-Time Shortest Path Algorithms for Networks Having Arbitrary Costs. 12.4 Multicommodity Flows. 12.5 Characterization of a Basis for the Multicommodity Minimal-Cost Flow Problem. 12.6 Synthesis of Multiterminal Flow Networks. Exercises. Notes and References. BIBLIOGRAPHY. INDEX.

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Book SynopsisUniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports schedulinTrade Review“Dr. Phillips has used other texts, but he is especially enthused with this book, influenced by student feedback. He says, “Algorithmic ideas are introduced at a pace that emphasizes and encourages intuitive understanding.” (Informs Journal on Computing, 1 June 2012) "The book is aimed at serving upper-undergraduate and graduate students of all fields as a comprehensive textbook or as a reference for studies on the subject." (Zentralblatt MATH, 2011) "The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problems; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development." (InfoTECH Spotlight - TMCnet, 8 February 2011) Table of ContentsPreface. 1. Introduction to Operations Research. 1.1 What is Deterministic Operations Research? 1.2 Introduction to Optimization Modeling. 1.3 Common Classes of Mathematical Programs. 1.4 About the Book. Exercises. 2. Linear Programming Modeling. 2.1 Resource Allocation Models. 2.2 Work Scheduling Models. 2.3 Models and Data. 2.4 Blending Models. 2.5 Production Process Models. 2.6 Multiperiod Models: Work Scheduling and Inventory. 2.7 Linearization of Special Nonlinear Models. 2.8 Various Forms of Linear Programs. 2.9 Network Models. Exercises. 3. Integer and Combinatorial Models. 3.1 Fixed-Charge Models. 3.2 Set Covering Models. 3.3 Models Using Logical Constraints. 3.4 Combinatorial Models. 3.5 Sports Scheduling and an Introduction to IP Solution Technques. Exercises. 4. Real-World Operations Research Applications: An Introduction. 4.1 Vehicle Routing Problems. 4.2 Facility Location and Network Design Models. 4.3 Applications in the Airline Industry. Exercises. 5. Introduction to Algorithm. 5.1 Exact and Heuristic Algorithms. 5.2 What to Ask When Designing Algorithms? 5.3 Constructive versus Local Search Algorithms. 5.4 How Good is our Heuristic Solution? 5.5 Example of a Local Search Method. 5.7 Other Heuristic Methods. 5.8 Designing Exact Methods: Optimality Conditions. Exercises. 6. Improving Search Algorithms and Comvexity. 6.1 Improving Search and Optimal Solutions. 6.2 Finding Better Solutions. 6.3 Convexity: When Does Improving Search Imply Global Optimality? 6.4 Farkas’ Lemma: When Can No Improving Feasible Direction be Found? Exercises. 7. Geometry and Algebra of Linear Programs. 7.1 Geometry and Algebra of “Corner Points”. 7.2 Fundamental Theorem of Linear Programming. 7.3 Linear Programs in Canonical Form. Exercises. 8. Solving Linear Programs: Simplex Method. 8.1 Simplex Method. 8.2 Making the Simplex Method More Efficient. 8.3 Convergence, Degeneracy, and the Simplex Method. 8.4 Finding an Initial Solution: Two-Phase Method. 8.5 Bounded Simplex Method. 8.6 Computational Issues. Exercises. 9. Linear Programming Duality. 9.1 Motivation: Generation Bounds. 9.2 Dual Linear Program. 9.3 Duality Theorems. 9.4 Another Interpretation of the Simplex Method. 9.5 Farkas’ Lemma Revisited. 9.6 Economic Interpretation of the Dual. 9.7 Another Duality Approach: Lagrangian Duality. Exercises. 10. Sensitivity Analysis of Linear Programs. 10.1 Graphical Sensitivity Analysis. 10.2 Sensitivity Analysis Calculations. 10.3 Use of Sensitivity Analysis. 10.4 Parametric Programming. Exercises. 11. Algorithmic Applications of Duality. 11.1 Dual Simplex Method. 11.2 Transportation Problem. 11.3 Column Generation. 11.4 Dantzig-Wolfe Decomposition. 11.5 Primal-Dual Interior Point Method. Exercises. 12. Network Optimization Algorithms. 12.1 Introduction to Network Optimization. 12.2 Shortest Path Problems. 12.3 Maximum Flow Problems. 12.4 Minimum Cost Network Flow Problems. Exercises. 13. Introduction to Integer Programming. 13.1 Basic Definitions and Formulations. 13.2 Relaxations and Bounds. 13.3 Preprocessing and Probing. 13.4 When are Integer Programs “Easy?’ Exercises. 14. Solving Integer Programs: Exact Methods. 14.1 Complete Enumeration. 14.2 Branch-and Bound Methods. 14.3 Valid Inequalities and Cutting Planes. 14.4 Gomory’s Cutting Plane Algorithm. 14.5 Valid Inequalities for 0-1 Knapsack Constraints. 14.6 Branch-and-Cut Algorithms. 14.7 Computational Issues. Exercises. 15. Solving Integer Programs: Modern Heuristic Techniques. 15.1 Review of Local Search Methods: Pros and Cons. 15.2 Simulated Annealing. 15.3 Tabu Search. 15.4 Genetic Algorithms. 15.5 GRASP Algorithms. Exercises. Appendix A: Background Review. A.1 Basic Notation. A.2 Graph Theory. A.3 Linear Algebra. Reference. Index.

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Book SynopsisA comprehensive, up-to-date text on linear programming. Covers all practical modeling, mathematical, geometrical, algorithmic, and computational aspects. Surveys recent developments in the field, including the Ellipsoid method. Includes extensive examples and exercises.Table of ContentsFormulation of Linear Programs. The Simplex Method. The Geometry of the Simplex Method. Duality in Linear Programming. Revised (Primal) Simplex Method. The Dual Simplex Method. Numerically Stable Forms of the Simplex Method. Parametric Linear Programs. Sensitivity Analysis. Degeneracy in Linear Programming. Bounded-Variable Linear Programs. The Decomposition Principle of Linear Programming. The Transportation Problem. Computational Complexity of the Simplex Algorithm. The Ellipsoid Method. Iterative Methods for Linear Inequalities and Linear Programs. Vector Minima. Index.

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Book SynopsisThis text is a coherent account of the science of decision making. It includes the models of operations research and those models of probability that relate to decision making. An emphasis in placed between these connections and relates these models to nearly all of the professions.Table of ContentsPreface. PART A: INTRODUCTION. The Science of Decision Making. Getting Started with Spreadsheets. PART B: USING LINEAR PROGRAMS. Analyzing Solutions of Linear Programs. A Survey of Linear Programs. Networks. Integer Programs. PART C: PROBABILITY FOR DECISION MAKING. Introduction to Probability Models. Discrete Random Variables. Decision Trees and Generalizations. Utility Theory and Decision Analysis. Continuous Random Variables. PART D: STOCHASTIC SYSTEMS. Inventory. Markov Chains. Queueing. Simulation. PART E: GAME THEORY. Game Theory. PART F: SOLVING LINEAR PROGRAMS. Solving Linear Equations. The Simplex Method. Duality. Appendix: Note on Excel. Index.

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Book SynopsisTheory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.Trade Review"...a comprehensive exposition of the theory of linear and integer programming...complementing the more practically oriented books." (Zentralblatt MATH, Vol. 970, 2001/20)Table of ContentsIntroduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear Diophantine Equations. Algorithms for Linear Diophantine Equations. Diophantine Approximation and Basis Reduction. POLYHEDRA, LINEAR INEQUALITIES, AND LINEAR PROGRAMMING. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming. The Structure of Polyhedra. Polarity, and Blocking and Anti-Blocking Polyhedra. Sizes and the Theoretical Complexity of Linear Inequalities and Linear Programming. The Simplex Method. Primal-Dual, Elimination, and Relaxation Methods. Khachiyan's Method for Linear Programming. The Ellipsoid Method for Polyhedra More Generally. Further Polynomiality Results in Linear Programming. INTEGER LINEAR PROGRAMMING. Introduction to Integer Linear Programming. Estimates in Integer Linear Programming. The Complexity of Integer Linear Programming. Totally Unimodular Matrices: Fundamental Properties and Examples. Recognizing Total Unimodularity. Further Theory Related to Total Unimodularity. Integral Polyhedra and Total Dual Integrality. Cutting Planes. Further Methods in Integer Linear Programming. References. Indexes.

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Book SynopsisMechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.Trade Review'The new book by Vohra is an excellent and most timely introduction into mechanism design. It offers a concise introduction to the theory of mechanism design, currently missing in the literature; it uses linear programming to great benefit to analyze the structure of incentives; and it provides a comprehensive account of the seminal results in auction and mechanism design. A splendid treatment for advanced undergraduate and graduate courses in economic theory!' Dirk Bergemann, Yale University'Rakesh Vohra's exposition of the theory of mechanism design is wonderfully transparent and elegant. This short book equips the reader with a remarkably deep and comprehensive understanding of this important subject.' Tilman Borgers, University of Michigan'Vohra convincingly demonstrates that linear programming can give a powerful and unified perspective on mechanism design, clarifying the ideas and methods underlying existing results, and leading in many cases to greater generality or new findings. Graduate students, researchers in other areas, and experienced mechanism designers will all benefit from this book, which will influence mechanism design research for years to come.' Andrew McLennan, University of Queensland'Professor Vohra's rigorous text is unique in showing how numerous central results in mechanism design can be unified using the methodology of linear programming. His treatment is elegant and original, and it touches the most recent research frontiers.' Benny Moldovanu, University of Bonn'Rakesh Vohra takes the reader from the basics of social choice theory and network flow problems to a deep understanding of optimal incentive systems for complex resource-allocation problems, using the mathematics of linear programming elegantly throughout the book.' Roger Myerson, University of Chicago and 2007 Nobel Laureate'By situating the fundamental questions of social choice, incentive compatibility, and auction design within the theory of linear programming, Vohra is able to address the modern themes of mechanism design in a cohesive manner. The result is inspiring, enjoyable, and extremely compelling.' David Parkes, Harvard University'This beautiful book provides an insightful and useful treatment of the fundamental theorems of social choice and mechanism design from the unifying and powerful perspective of linear programming. A terrific read covering a broad range of topics including a serious and rare treatment of multidimensional mechanism design.' Phillip J. Reny, University of Chicago'The book does not assume any prior knowledge of mechanism design, but requires some familiarity with game theory, linear programming and convex analysis. As such, it is well suited to students and graduates of economic courses, but also to researchers and experienced mechanism designers.' Vangelis Grigoroudis, Zentralblatt MATHTable of Contents1. Introduction; 2. Arrow's theorem and its consequences; 3. Network flow problem; 4. Incentive compatibility; 5. Efficiency; 6. Revenue maximization; 7. Rationalizability.

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Book SynopsisIndividuals and families make key decisions that impact many aspects of financial stability and determine the future of the economy. These decisions involve balancing current sacrifice against future benefits. This book is about modeling this individual or family-based decision making using an optimizing dynamic programming model.Trade Review"Forward-Looking Decision Making provides interesting applications of the dynamic programming approach for analyzing individual decisions that balance current and future welfare. The subjects are timely and the book contains a good selection of topics, united by a common analytical theme."—John Ermisch, University of EssexTable of ContentsForeword vii Preface ix Chapter 1: Basic Analysis of Forward-Looking Decision Making 1 1.1 The Dynamic Program 1 1.2 Approximation 5 1.3 Stationary Case 6 1.4 Markov Representation 7 1.5 Distribution of the Stochastic Driving Force 9 Chapter 2: Research on Properties of Preferences 10 2.1 Research Based on Marshallian and Hicksian Labor Supply Functions 13 2.2 Risk Aversion 15 2.3 Intertemporal Substitution 17 2.4 Frisch Elasticity of Labor Supply 19 2.5 Consumption-Hours Complementarity 20 Chapter 3: Health 23 3.1 The Issues 23 3.2 Basic Facts 25 3.3 Basic Model 26 3.4 The Full Dynamic-Programming Model 31 3.5 The Health Production Function 35 3.6 Preference Parameters 36 3.7 Solving the Model 37 3.8 Concluding Remarks 38 Chapter 4: Insurance 42 4.1 The Model 43 4.2 Calibration 45 4.3 Results 46 Chapter 5: Employment 50 5.1 Insurance 52 5.2 Dynamic Labor-Market Equilibrium 53 5.3 The Employment Function 58 5.4 Econometric Model 59 5.5 Properties of the Data 64 5.6 Results 65 5.7 Concluding Remarks 69 Chapter 6: Idiosyncratic Risk 70 6.1 The Joint Distribution of Lifetime and Exit Value 73 6.2 Economic Payoffs to Entrepreneurs 74 6.3 Entrepreneurs in Aging Companies 82 6.4 Concluding Remarks 85 Chapter 7: Financial Stability with Government-Guaranteed Debt 87 7.1 Introduction 87 7.2 Options 92 7.3 Model 94 7.4 Calibration 100 7.5 Equilibrium 101 7.6 Roles of Key Parameters 113 7.7 Concluding Remarks 115 7.8 Appendix: Value Functions 116 References 119 Index 123

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Book SynopsisDevelops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents a treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures.Trade ReviewWassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics "The monograph is an excellent up-to-date authoritative reference covering original results which are presented in a rigorous, unified framework with examples... The book will be useful primarily to applied mathematicians, control theorists and engineers, and anyone dealing with Lyapunov stability and control of nonlinear interconnected dynamic systems."--Lubomir Bakule, Zentralblatt MATHTable of ContentsPreface xiii CHAPTER 1. Introduction 1 1.1 Large-Scale Interconnected Dynamical Systems 1 1.2 A Brief Outline of the Monograph 5 CHAPTER 2. Stability Theory via Vector Lyapunov Functions 9 2.1 Introduction 9 2.2 Notation and Definitions 9 2.3 Quasi-Monotone and Essentially Nonnegative Vector Fields 10 2.4 Generalized Differential Inequalities 14 2.5 Stability Theory via Vector Lyapunov Functions 18 2.6 Discrete-Time Stability Theory via Vector Lyapunov Functions 34 CHAPTER 3. Large-Scale Continuous-Time Interconnected Dynamical Systems 45 3.1 Introduction 45 3.2 Vector Dissipativity Theory for Large-Scale Nonlinear Dynamical Systems 46 3.3 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Nonlinear Dynamical Systems 61 3.4 Specialization to Large-Scale Linear Dynamical Systems 68 3.5 Stability of Feedback Interconnections of Large-Scale Nonlinear Dynamical Systems 71 CHAPTER 4. Thermodynamic Modeling of Large-Scale Interconnected Systems 75 4.1 Introduction 75 4.2 Conservation of Energy and the First Law of Thermodynamics 75 4.3 Nonconservation of Entropy and the Second Law of Thermodynamics 79 4.4 Semistability and Large-Scale Systems 82 4.5 Energy Equipartition 86 4.6 Entropy Increase and the Second Law of Thermodynamics 88 4.7 Thermodynamic Models with Linear Energy Exchange 90 CHAPTER 5. Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions 93 5.1 Introduction 93 5.2 Control Vector Lyapunov Functions 94 5.3 Stability Margins, Inverse Optimality, and Vector Dissipativity 99 5.4 Decentralized Control for Large-Scale Nonlinear Dynamical Systems 102 CHAPTER 6. Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions 107 6.1 Introduction 107 6.2 Finite-Time Stability via Vector Lyapunov Functions 108 6.3 Finite-Time Stabilization of Large-Scale Dynamical Systems 114 6.4 Finite-Time Stabilization for Large-Scale Homogeneous Systems 119 6.5 Decentralized Control for Finite-Time Stabilization of Large-Scale Systems 121 CHAPTER 7. Coordination Control for Multiagent Interconnected Systems 127 7.1 Introduction 127 7.2 Stability and Stabilization of Time-Varying Sets 129 7.3 Control Design for Multivehicle Coordinated Motion 135 7.4 Stability and Stabilization of Time-Invariant Sets 141 7.5 Control Design for Static Formations 144 7.6 Obstacle Avoidance in Multivehicle Coordination 145 CHAPTER 8. Large-Scale Discrete-Time Interconnected Dynamical Systems 153 8.1 Introduction 153 8.2 Vector Dissipativity Theory for Discrete-Time Large-Scale Nonlinear Dynamical Systems 154 8.3 Extended Kalman-Yakubovich-Popov Conditions for Discrete- Time Large-Scale Nonlinear Dynamical Systems 168 8.4 Specialization to Discrete-Time Large-Scale Linear Dynamical Systems 173 8.5 Stability of Feedback Interconnections of Discrete-Time Large-Scale Nonlinear Dynamical Systems 177 CHAPTER 9. Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems 181 9.1 Introduction 181 9.2 Conservation of Energy and the First Law of Thermodynamics 182 9.3 Nonconservation of Entropy and the Second Law of Thermodynamics 187 9.4 Nonconservation of Ectropy 189 9.5 Semistability of Discrete-Time Thermodynamic Models 191 9.6 Entropy Increase and the Second Law of Thermodynamics 198 9.7 Thermodynamic Models with Linear Energy Exchange 200 CHAPTER 10. Large-Scale Impulsive Dynamical Systems 211 10.1 Introduction 211 10.2 Stability of Impulsive Systems via Vector Lyapunov Functions 213 10.3 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems 224 10.4 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Impulsive Dynamical Systems 249 10.5 Specialization to Large-Scale Linear Impulsive Dynamical Systems 259 10.6 Stability of Feedback Interconnections of Large-Scale Impulsive Dynamical Systems 264 CHAPTER 11. Control Vector Lyapunov Functions for Large-Scale Impulsive Systems 271 11.1 Introduction 271 11.2 Control Vector Lyapunov Functions for Impulsive Systems 272 11.3 Stability Margins and Inverse Optimality 279 11.4 Decentralized Control for Large-Scale Impulsive Dynamical Systems 284 CHAPTER 12. Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems 289 12.1 Introduction 289 12.2 Finite-Time Stability of Impulsive Dynamical Systems 289 12.3 Finite-Time Stabilization of Impulsive Dynamical Systems 297 12.4 Finite-Time Stabilizing Control for Large-Scale Impulsive Dynamical Systems 300 CHAPTER 13. Hybrid Decentralized Maximum Entropy Control for Large-Scale Systems 305 13.1 Introduction 305 13.2 Hybrid Decentralized Control and Large-Scale Impulsive Dynamical Systems 306 13.3 Hybrid Decentralized Control for Large-Scale Dynamical Systems 313 13.4 Interconnected Euler-Lagrange Dynamical Systems 319 13.5 Hybrid Decentralized Control Design 323 13.6 Quasi-Thermodynamic Stabilization and Maximum Entropy Control 327 13.7 Hybrid Decentralized Control for Combustion Systems 335 13.8 Experimental Verification of Hybrid Decentralized Controller 341 CHAPTER 14. Conclusion 351 Bibliography 353 Index 367

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Book SynopsisHybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. This title unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems.Trade Review"The book is carefully written and contains many examples. It will be a good resource for both researchers already familiar with hybrid systems and those starting from scratch."--Daniel Liberzon, Mathematical Reviews Clippings "The book presents a clean and self-contained exposition of hybrid systems, starting from the elementary definitions, continuing with the basic tools and finishing with more recent contributions in the literature."--Marco Castrillon Lopez, European Mathematical SocietyTable of ContentsPreface ix Chapter 1: Introduction 1 1.1 The modeling framework 1 1.2 Examples in science and engineering 2 1.3 Control system examples 7 1.4 Connections to other modeling frameworks 15 1.5 Notes 22 Chapter 2 The solution concept 25 2.1 Data of a hybrid system 25 2.2 Hybrid time domains and hybrid arcs 26 2.3 Solutions and their basic properties 29 2.4 Generators for classes of switching signals 35 2.5 Notes 41 Chapter 3 Uniform asymptotic stability, an initial treatment 43 3.1 Uniform global pre-asymptotic stability 43 3.2 Lyapunov functions 50 3.3 Relaxed Lyapunov conditions 60 3.4 Stability from containment 64 3.5 Equivalent characterizations 68 3.6 Notes 71 Chapter 4 Perturbations and generalized solutions 73 4.1 Differential and difference equations 73 4.2 Systems with state perturbations 76 4.3 Generalized solutions 79 4.4 Measurement noise in feedback control 84 4.5 Krasovskii solutions are Hermes solutions 88 4.6 Notes 94 Chapter 5 Preliminaries from set-valued analysis 97 5.1 Set convergence 97 5.2 Set-valued mappings 101 5.3 Graphical convergence of hybrid arcs 107 5.4 Differential inclusions 111 5.5 Notes 115 Chapter 6 Well-posed hybrid systems and their properties 117 6.1 Nominally well-posed hybrid systems 117 6.2 Basic assumptions on the data 120 6.3 Consequences of nominal well-posedness 125 6.4 Well-posed hybrid systems 132 6.5 Consequences of well-posedness 134 6.6 Notes 137 Chapter 7 Asymptotic stability, an in-depth treatment 139 7.1 Pre-asymptotic stability for nominally well-posed systems 141 7.2 Robustness concepts 148 7.3 Well-posed systems 151 7.4 Robustness corollaries 153 7.5 Smooth Lyapunov functions 156 7.6 Proof of robustness implies smooth Lyapunov functions 161 7.7 Notes 167 Chapter 8 Invariance principles 169 8.1 Invariance and omega-limits 169 8.2 Invariance principles involving Lyapunov-like functions 170 8.3 Stability analysis using invariance principles 176 8.4 Meagre-limsup invariance principles 178 8.5 Invariance principles for switching systems 181 8.6 Notes 184 Chapter 9 Conical approximation and asymptotic stability 185 9.1 Homogeneous hybrid systems 185 9.2 Homogeneity and perturbations 189 9.3 Conical approximation and stability 192 9.4 Notes 196 Appendix: List of Symbols 199 Bibliography 201 Index 211

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Book SynopsisIntroduces a theoretical entity: Agent_Zero. This title weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others.Trade Review"Agent Zero offers a solution to some of social science's great puzzles. Its behavioral basis is the interplay of emotion, cognition, and network contagion effects. It elegantly explains why so many human actions are so manifestly dysfunctional, and why some are downright evil."—George Akerlof, Nobel Laureate in Economics"Rarely has a book stimulated me intellectually as much as this one. Particularly exciting is the incorporation of agents who feel (affect) and deliberate, as well as influence one another through social interaction. Epstein is a brilliantly creative scholar and the range of applications showcased here is stunning. In sum, this is a pathbreaking book."—Paul Slovic, University of Oregon"Joshua Epstein proposes a parsimonious but powerful model of individual behavior that can generate an extraordinary range of group behaviors, including mob violence, manias and financial panics, rebellions, network dynamics, and a host of other complex social phenomena. This is a highly original, beautifully conceived, and important book."—Peyton Young, University of Oxford"In social science generally and most notably in economics, the rational actor model has long been the benchmark for policy analysis and institutional design. Epstein now offers a worthy alternative: Agent_Zero, a mathematically and computationally tractable agent whose inner workings are grounded in neuroscience. Much like you and me, Agent_Zero is influenced by emotion, reason, and social pressures. Epstein demonstrates that collections of Agent Zeros perform amazingly like real groups, teams, and societies and can therefore serve as the fundamental building blocks for what he calls Generative Social Science. The rational actor now has a true competitor. Agent_Zero is a major advance."—Scott Page, University of Michigan"This is social science based on how our brains actually work. Epstein's computerized 'agents' can feel passion and fear, and can influence each other emotionally. And when they interact, we see many of the realities of social life, from the dynamics of juries to racist violence to Arab springs. A remarkable and original piece of work."—W. Brian Arthur, Santa Fe InstituteTable of ContentsForeword xi Preface xiii Acknowledgments xv INTRODUCTION 1 MOTIVATION 1 Generate Social Dynamics 2 A Core Target 2 THE MODEL COMPONENTS 5 Model Overview 6 Skeletal Equation 8 Specific Components 9 ORGANIZATION 10 Part I: Mathematical Model 10 Part II: Agent-Based Model 11 Part III: Extensions 13 Replicability and Research Resources on the Princeton University Press Website 16 Part IV: Future Research and Conclusions 17 PART 1. MATHEMATICAL MODEL 19 I.1. THE PASSIONS: FEAR CONDITIONING 19 Fear Circuitry and the Perils of Fitness 20 Nomenclature of Conditioning 29 The Rescorla-Wagner Model 33 Social Examples 37 Fear Extinction 41 I.2. REASON: THE COGNITIVE COMPONENT 46 I.3. THE SOCIAL COMPONENT 51 Simple Version of the Core Target 55 Examples of Fear Contagion 57 Mechanisms of Fear Contagion 59 Conformist Empirical Estimates 63 Generalizing Rescorla-Wagner 67 The Central Case 69 Tolstoy: The First Agent Modeler 71 A Mathematical Aside on Social Norms as Vector Fields 74 Extinction of Majorities 78 I.4. INTERIM CONCLUSIONS 80 PART II. AGENT-BASED COMPUTATIONAL MODEL 81 Affective Component 84 "Rational" Component 85 Social Component 88 Action 89 Pseudocode 89 II.1. COMPUTATIONAL PARABLES 90 Parable 1: The Slaughter of Innocents through Dispositional Contagion 90 Parable 2: Agent_Zero Initiates: Leadership as Susceptibility to Dispositional Contagion 94 Run 3. Information Cuts Both Ways 96 Run 4. A Day in the Life of Agent_Zero: How Affect and Probability Can Change on Different Time Scales 98 Run 5. Lesion Studies 102 PART III. EXTENSIONS 107 III.1. ENDOGENOUS DESTRUCTIVE RADIUS 107 III.2. AGE AND IMPULSE CONTROL 109 III.3. FIGHT VS. FLIGHT 110 Case 1: Fight 111 Case 2: Flight 112 Capital Flight 114 III.4. REPLICATING THE Latane-DARLEY EXPERIMENT 114 Threshold Imputation 115 The Dialogue 118 III.5. MEMORY 118 III.6. COUPLINGS: ENTANGLEMENT OF PASSION AND REASON 122 Mathematical Treatment 124 III.7.ENDOGENOUS DYNAMICS OF CONNECTION STRENGTH 128 Affective Homophily 128 General Setup 130 Agent-Based Model: Nonequlibrium Dynamics 135 III.8. GROWING THE 2011 ARAB SPRING 138 III.9. JURY PROCESSES 143 Phase 1. Public Phase 143 Phase 2. Courtroom Trial Phase 145 Phase 3. Jury Phase 147 III.10. EMERGENT DYNAMICS OF NETWORK STRUCTURE 152 Network Structure Dynamics as a Poincare Map 153 Relation to Literature 159 III.11. MULTIPLE SOCIAL LEVELS 160 Agent_Zero as Witness to History 161 III.12. THE 18TH BRUMAIRE OF AGENT_ZERO 165 III.13. INTRODUCTION OF PRICES AND SEASONAL ECONOMIC CYCLES 168 Prices 168 A Christmas Story 173 III.14. SPIRALS OF MUTUAL ESCALATION 176 PART IV. FUTURE RESEARCH AND CONCLUSION 181 IV.1. FUTURE RESEARCH 181 IV.2. CONCLUSION 187 Civil Violence 187 Economics 188 Health Behavior 189 Psychology 190 Jury Dynamics 191 The Formation and Dynamics of Networks 191 Mutual Escalation Dynamics 192 Birth and Intergenerational Transmission 192 IV.3. TOWARD NEW GENERATIVE FOUNDATIONS 192 Appendix I. Threshold Imputation Bounds 195 Appendix II. Mathematica Code 197 Appendix III. Agent_Zero NetLogo Source Code 213 Appendix IV. Parameter Settings for Model Runs 221 References 227 Index 243

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Book SynopsisTrade Review“Innovative, mathematically exact, and very well written. Garoche is a rare resource, and his book will enrich the knowledge of both the computer-science and control-systems communities.”—Eric Feron, Georgia Institute of Technology "This book makes a timely contribution at the crossroads of formal computer science, optimization, and control. It should be of interest to computer scientists and control engineers."—Didier Henrion, LAAS-CNRS Toulouse and Czech Technical University in Prague“A pleasure to read. Garoche’s excellent and timely book presents state-of-the-art methods building on convex optimization to perform static analysis for control systems and software.”—Taylor Johnson, Vanderbilt University

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Book SynopsisThis book presents simple, elegant methods for dealing, both in theory and in application, with a variety of problems that have formulations in terms of flows in capacity-constrained networks. Since the theoretical considerations lead in all cases to computationally efficient solution procedures, the hook provides a common meeting ground for personTable of Contents*Frontmatter, pg. i*PREFACE, pg. vii*ACKNOWLEDGMENTS, pg. ix*CONTENTS, pg. xi*CHAPTER I. STATIC MAXIMAL FLOW, pg. 1*CHAPTER II. FEASIBILITY THEOREMS AND COMBINATORIAL APPLICATIONS, pg. 36*CHAPTER III. MINIMAL COST FLOW PROBLEMS, pg. 93*CHAPTER IV. MULTI-TERMINAL MAXIMAL FLOWS, pg. 173*INDEX, pg. 193*Backmatter, pg. 195

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Book SynopsisThis book is one of its own kind. It is not an encyclopedia or a hands-on tutorial that traps readers in the tutorial hell. It is a distillation of just one common Python user's learning experience. The experience is packaged with exceptional teaching techniques, careful dependence unraveling and, most importantly, passion.Learning Advanced Python by Studying Open Source Projects helps readers overcome the difficulty in their day-to-day tasks and seek insights from solutions in famous open source projects. Different from a technical manual, this book mixes the technical knowledge, real-world applications and more theoretical content, providing readers with a practical and engaging approach to learning Python.Throughout this book, readers will learn how to write Python code that is efficient, readable and maintainable, covering key topics such as data structures, algorithms, object-oriented programming and more. The author's passion for Python shines through in tTable of ContentsIntroductionChapter 1 ◾ The Data Model of PythonChapter 2 ◾ Selected Topics of Python ClassesChapter 3 ◾ Concurrency in PythonChapter 4 ◾ Asynchronous Programming in PythonChapter 5 ◾ Power Up Your Python FunctionsChapter 6 ◾ Selected OOP Design Best PracticesChapter 7 ◾ Testing in a Pistachio Shell

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Book SynopsisThe unique feature of this compact student''s introduction to Mathematica and the Wolfram Language is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.Trade Review'This book is an easy-to-read introduction to Mathematica. It is interspersed with helpful hints that make interacting with Mathematica more efficient and examples to test the reader's comprehension. This book is good for learning how to use Mathematica to graph functions, perform algebraic manipulation, and approach topics from calculus and linear algebra. This new version shines some light on entity objects and accessing Wolfram's curated data which is needed because their structure is unintuitive and because of their growing prominence in the Wolfram ecosystem. The new final chapter on 3D printing gives readers the tools to quickly design and 3D print physical objects that embody mathematical surfaces. These two additions showcase recent advances in the Wolfram Language and ensure that the whole book remains relevant and up to date.' Christopher Hanusa, Queens College, City University of New York'Mathematica has the power to unravel some of the current mysteries of mathematics – but only if you know how to ask it the right questions. The 3rd edition of The Student's Introduction to Mathematica and the Wolfram Language can be your well-used guide for such exploration. Beginning and experienced Mathematica users will easily learn from the pages of this book especially given the recent changes to Mathematica. Even more, the 3rd edition moves into a new dimension, giving details on 3D printing! Grab one for yourself and another for a student you know.' Tim Chartier, Davidson College, North Carolina'This text, including the exercises and solutions, is written in a student-friendly style … Unlike most tutorial introductions to Mathematica, the authors go to significant lengths to provide explanations and rationales underlying what a newcomer would likely find confusing … I believe that this book would be a useful addition to any student's library in a college or university that uses Mathematica.' Marvin Schaefer, MAA ReviewsTable of ContentsPreface; 1. Getting started; 2. Working with Mathematica®; 3. Functions and their graphs; 4. Algebra; 5. Calculus; 6. Multivariable calculus; 7. Linear algebra; 8. Programming; 9. 3D printing; Index.

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Book SynopsisThe 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, whTable of ContentsPreface PART 1 1 Introduction 1.1 The Concept of a Model 1.2 Mathematical Programming Models 2 Solving Mathematical Programming Models 2.1 Algorithms and Packages 2.2 Practical Considerations 2.3 Decision Support and Expert Systems 2.4 Constraint Programming 3 Building Linear Programming Models 3.1 The Importance of Linearity 3.2 Defining Objectives 3.3 Defining Constraints 3.4 How to Build a Good Model 3.5 The Use of Modelling Languages 4 Structured Linear Programming Models 4.1 Multiple Plant, Product, and Period Models 4.2 Stochastic Programming Models 4.3 Decomposing a Large Model 5 Applications and Special Types of Mathematical Programming Model 5.1 Typical Applications 5.2 Economic Models 5.3 Network Models 5.4 Converting Linear Programs to Networks 6 Interpreting and Using the Solution of a Linear Programming Model 6.1 Validating a Model 6.2 Economic Interpretations 6.3 Sensitivity Analysis and the Stability of a Model 6.4 Further Investigations Using a Model 6.5 Presentation of the Solutions 7 Non-linear Models 7.1 Typical Applications 7.2 Local and Global Optima 7.3 Separable Programming 7.4 Converting a Problem to a Separable Model 8 Integer Programming 8.1 Introduction 8.2 The Applicability of Integer Programming 8.3 Solving Integer Programming Models 9 Building Integer Programming Models I 9.1 The Uses of Discrete Variables 9.2 Logical Conditions and Zero—One Variables 9.3 Special Ordered Sets of Variables 9.4 Extra Conditions Applied to Linear Programming Models 9.5 Special Kinds of Integer Programming Model 9.6 Column Generation 10 Building Integer Programming Models II 10.1 Good and Bad Formulations 10.2 Simplifying an Integer Programming Model 10.3 Economic Information Obtainable by Integer Programming 10.4 Sensitivity Analysis and the Stability of a Model 10.5 When and How to Use Integer Programming 11 The Implementation of a Mathematical Programming System of Planning 11.1 Acceptance and Implementation 11.2 The Unification of Organizational Functions 11.3 Centralization versus Decentralization 11.4 The Collection of Data and the Maintenance of a Model PART 2 12 The Problems 12.1 Food Manufacture 1 When to buy and how to blend 12.2 Food Manufacture 2 Limiting the number of ingredients and adding extra conditions 12.3 Factory Planning 1 What to make, on what machines, and when 12.4 Factory Planning 2 When should machines be down for maintenance 12.5 Manpower Planning How to recruit, retrain, make redundant, or overman 12.6 Refinery Optimization How to run an oil refinery 12.7 Mining Which pits to work and when to close them down 12.8 Farm Planning How much to grow and rear 12.9 Economic Planning How should an economy grow 12.10 Decentralization How to disperse offices from the capital 12.11 Curve Fitting Fitting a curve to a set of data points 12.12 Logical Design Constructing an electronic system with a minimum number of components 12.13 Market Sharing Assigning retailers to company divisions 12.14 Opencast Mining How much to excavate 12.15 Tariff Rates (Power Generation) How to determine tariff rates for the sale of electricity 12.16 Hydro Power How to generate and combine hydro and thermal electricity generation 12.17 Three-dimensional Noughts and Crosses A combinatorial problem 12.18 Optimizing a Constraint Reconstructing an integer programming constraint more simply 12.19 Distribution 1 Which factories and depots to supply which customers 12.20 Depot Location (Distribution 2) Where should new depots be built 12.21 Agricultural Pricing What prices to charge for dairy products 12.22 Efficiency Analysis How to use data envelopment analysis to compare efficiencies of garages 12.23 Milk Collection How to route and assign milk collection lorries to farms 12.24 Yield Management What quantities of airline tickets to sell at what prices and what times 12.25 Car Rental 1 How many cars to own and where to locate them 12.26 Car Rental 2 Where should repair capacity be increased 12.27 Lost Baggage Distribution Which vehicles should go to which customers and in what order 12.28 Protein Folding How a string of Amino Acids is likely to fold 12.29 Protein Comparison How similar are two proteins PART 3 13 Formulation and Discussion of Problems 13.1 Food Manufacture 1 13.2 Food Manufacture 2 13.3 Factory Planning 1 13.4 Factory Planning 2 13.5 Manpower Planning 13.6 Refinery Optimization 13.7 Mining 13.8 Farm Planning 13.9 Economic Planning 13.10 Decentralization 13.11 Curve Fitting 13.12 Logical Design 13.13 Market Sharing 13.14 Opencast Mining 13.15 Tariff Rates (Power Generation) 13.16 Hydro Power 13.17 Three-dimensional Noughts and Crosses 13.18 Optimizing a Constraint 13.19 Distribution 1 13.20 Depot Location (Distribution 2) 13.21 Agricultural Pricing 13.22 Efficiency Analysis 13.23 Milk Collection 13.24 Yield Management 13.25 Car Rental 1 13.26 Car Rental 2 13.27 Lost Baggage Distribution 13.28 Protein Folding 13.29 Protein Comparison PART 4 14 Solutions to Problems 14.1 Food Manufacture 1 14.2 Food Manufacture 2 14.3 Factory Planning 1 14.4 Factory Planning 2 14.5 Manpower Planning 14.6 Refinery Optimization 14.7 Mining 14.8 Farm Planning 14.9 Economic Planning 14.10 Decentralization 14.11 Curve Fitting 14.12 Logical Design 14.13 Market Sharing 14.14 Opencast Mining 14.15 Tariff Rates (Power Generation) 14.16 Hydro Power 14.17 Three-dimensional Noughts and Crosses 14.18 Optimizing a Constraint 14.19 Distribution 1 14.20 Depot Location (Distribution 2) 14.21 Agricultural Pricing 14.22 Efficiency Analysis 14.23 Milk Collection 14.24 Yield Management 14.25 Car Rental 1 14.26 Car Rental 2 14.27 Lost Baggage Distribution 14.28 Protein Folding 14.29 Protein Comparison References Author Index Subject Index

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Book SynopsisOptimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; foundTrade Review'This delightful compact tome gives the reader all the results they should have in their pocket to contribute to optimization and statistical learning. With the clean, elegant derivations of many of the foundational optimization methods underlying modern large-scale data analysis, everyone from students just getting started to researchers knowing this book inside and out will be well-positioned for both using the algorithms and developing new ones for machine learning, optimization, and statistics.' John C. Duchi, Stanford University'Optimization algorithms play a vital role in the rapidly evolving field of machine learning, as well as in signal processing, statistics and control. Numerical optimization is a vast field, however, and a student wishing to learn the methods required in the world of data science could easily get lost in the literature. This book does a superb job of presenting the most important algorithms, providing both their mathematical foundations and lucid motivations for their development. Written by two of the foremost experts in the field, this book gently guides a reader without prior knowledge of optimization towards the methods and concepts that are central in modern data science applications.' Jorge Nocedal, Northwestern University'This timely introductory book gives a rigorous view of continuous optimization techniques which are being used in machine learning. It is an excellent resource for those who are interested in understanding the mathematical concepts behind commonly used machine learning techniques.' Shai Shalev-Shwartz, Hebrew University of Jerusalem'This textbook is a much-needed exposition of optimization techniques, presented with conciseness and precision, with emphasis on topics most relevant for data science and machine learning applications. I imagine that this book will be immensely popular in university courses across the globe, and become a standard reference used by researchers in the area.' Amitabh Basu, Johns Hopkins UniversityTable of Contents1. Introduction; 2. Foundations of smooth optimization; 3. Descent methods; 4. Gradient methods using momentum; 5. Stochastic gradient; 6. Coordinate descent; 7. First-order methods for constrained optimization; 8. Nonsmooth functions and subgradients; 9. Nonsmooth optimization methods; 10. Duality and algorithms; 11. Differentiation and adjoints.

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Book SynopsisThis monograph is aimed at presenting smooth and unified generalized fractional programming (or a program with a finite number of constraints). Under the current interdisciplinary computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of its multi-facet applications and empowerment for real world problems that can be handled by transforming them into generalized fractional programming problems. Problems of this type have been applied for the modeling and analysis of a wide range of theoretical as well as concrete, real world, practical problems. More specifically, generalized fractional programming concepts and techniques have found relevance and worldwide applications in approximation theory, statistics, game theory, engineering design (earthquake-resistant design of structures, design of control systems, digital filters, electronic circuits, etc.), boundary value problems, defect minimization for operator equations, geometry, random graphs, graphs related to Newton flows, wavelet analysis, reliability testing, environmental protection planning, decision making under uncertainty, geometric programming, disjunctive programming, optimal control problems, robotics, and continuum mechanics, among others. It is highly probable that among all industries, especially for the automobile industry, robots are about to revolutionize the assembly plants forever. That would change the face of other industries toward rapid technical innovation as well. The main focus of this monograph is to empower graduate students, faculty and other research enthusiasts for more accelerated research advances with significant applications in the interdisciplinary sense without borders. The generalized fractional programming problems have a wide range of real-world problems, which can be transformed in some sort of a generalized fractional programming problem. Consider fractional programs that arise from management decision science; by analyzing system efficiency in an economical sense, it is equivalent to maximizing system efficiency leading to fractional programs with occurring objectives: Maximizing productivity; Maximizing return on investment; Maximizing return/ risk; Minimizing cost/time; Minimizing output/input. The authors envision that this monograph will uniquely present the interdisciplinary research for the global scientific community (including graduate students, faculty, and general readers). Furthermore, some of the new concepts can be applied to duality theorems based on the use of a new class of multi-time, multi-objective, variational problems as well.

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Book SynopsisCompressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing.An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate.The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.

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Book SynopsisNumerical Linear Algebra and Optimization covers the fundamentals of closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite-precision environment are derived and analyzed. In 1991, when the book first appeared, these topics were rarely taught with a unified perspective, and, somewhat surprisingly, this remains true almost 30 years later. As a result, some of the material in this book can be difficult to find elsewhere—in particular, techniques for updating the LU factorization, descriptions of the simplex method applied to all-inequality form, and the analysis of what happens when using an approximate inverse to solve Ax=b.This book is appropriate for students who want to learn about numerical techniques for solving linear systems and/or linear programming using the simplex method.

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

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Book SynopsisLinear programming (LP), as a specific case of mathematical programming, has been widely encountered in a broad class of scientific disciplines and engineering applications. In view of its fundamental role, the solution of LP has been investigated extensively for the past decades. Due to the parallel-distributed processing nature and circuit-implementation convenience, the neurodynamic solvers based on recurrent neural network (RNN) have been regarded as powerful alternatives to online computation. This book discusses how linear programming is used to plan and schedule the workforce in an emergency room; the neurodynamic solvers, robotic applications, and solution non-uniqueness of linear programming; the mathematical equivalence of simple recourse and chance constraints in linear stochastic programming; and provides a decomposable linear programming model for energy supply chains.

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Book SynopsisThis book studies the methods for solving non-linear, partial differential equations that have physical meaning, and soliton theory with applications. Specific descriptions on the formation mechanism of soliton solutions of non-linear, partial differential equations are given, and some methods for solving this kind of solution such as the Inverse Scattering Transform method, Backlund Transformation method, Similarity Reduction method and several kinds of function transformation methods are introduced. Integrability of non-linear, partial differential equations is also discussed. This book is suitable for graduate students whose research fields are in applied mathematics, applied physics and non-linear science-related directions as a textbook or a research reference book. This book is also useful for non-linear science researchers and teachers as a reference book. The characteristics of this book are: 1. The author provides clear concepts, rigorous derivation, thorough reasoning, and rigorous logic in the book. Since the research boom of non-linear, partial differential equations was rising in the 1960s, the research on non-linear, partial differential equations and soliton theory has only been several decades, which can be described as a very young discipline compared to the other branches in mathematics. Although there are a few related books, they are mostly in highly specialised interdisciplinary areas. There is no book which is suitable for cross-disciplines and for people with college level mathematics and college physics background. This book fills that gap; 2. The book is easy to be understood by readers since it provides step-by-step approaches. All results in the book have been deduced and collated by the author to make sure that they are correct and perfect; 3. The derivation from the physical models to mathematical models is emphasised in the book. In mathematical physics, we cannot just simply consider the mathematical problems without a physical image, which often plays the key role for understanding the mathematical problems; 4. Mathematical transformation methods are provided. The basic idea of various methods for solving non-linear, partial differential equations is to simplify the complex equations into simple ones through some transformations or decompositions. However, we cannot find any patterns for using such transformations or decompositions, and certain conjectures and assumptions have to be used. However, the skill and the logic of using the transformations and decompositions are very important to researchers in this field.

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Book SynopsisThe 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.Table of Contents

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Book Synopsis Der erste Kontakt.- Routenplanung, was ist das?- Gestatten, Graph.- Gewicht ist Pflicht.- Eine ungefährliche Explosion.- Kurzstrecke oder nicht? Das ist hier die Frage!- Lokal entscheiden, global optimieren.- Am Anfang war der Input.- Negativ ist negativ,- Gute Zeiten, schlechte Zeiten.- Weibliche Intuition.- Die Arbeit vor der Arbeit.- Bäumchen wechsle dich!- Prim, ohne Zahlen.- Nimm, was du kriegen kannst!.- Arbor-was?.- Studieren geht über flanieren.- Spannung ohne Strom.- Eulersch oder nicht, was für ein Gedicht.- Euler und der Nikolaus.- Heute flaniert die Müllabfuhr.- Paarungszeit.- Post aus China.- Schach-Matt?.- Platonische Liebe?.- Notorisch Problematisch.- Not eines Handlungsreisenden.- Weniger ist mehr.-150-prozentig.- Bonsai.- Gar nicht so platonisch.- Der Erfolg des Handlungsreisenden.Trade Review "Da haben sich zwei Autoren etwas ganz Originelles ausgedacht. Mittels eines imaginären Dialogs zwischen einem 15-jährigen Mädchen und einem sprechenden Computer wird der Leser in die Grundlagen der mathematischen Modellierung eingeführt. Dabei geht es um wirkliche Probleme, die - ausgehend von einer alltäglichen Frage - im Laufe der Gespräche immer mehr in eine mathematisch fassbare Form gebracht werden." Neue Züricher Zeitung "Der Text ist spannend aufgebaut, auch für jüngeres Publikum leicht lesbar geschrieben und er bietet tatsächlich eine schülerfreundliche Einführung in die Algorithmik verbunden mit Graphentheorie."Elemente der Mathematik "Ein erfreulich erfrischendes Buch über Probleme der Mathematik." Zeitschrift des Bayrischen Philologenverbandes "Möge ihr (der Autoren) Beispiel Schule machen. Um ihm zu folgen, bedarf es nicht unabdingbar des hier vorgeführten erzählerischen Talents. ... Wichtig aber ist die ansteckende Mischung aus fachlicher Versiertheit, persönlicher Begeisterung und Hinwendung zum Adressaten." Prof. Lisa Hefendehl-Hebecker in Zentralblatt für Didaktik der Mathematik "... Das Buch ist ein Genuss nicht nur fur diejenigen, die mit den Themen erstmalig in Berührung kommen. Studierende können einen Zugang zum Gebiet effiziente Algorithmen gewinnen und auch Erfahrene werden die Zeit, in der sie das Buch in Händen halten, nicht bereuen. Wir aus der Informatikgemeinde sollten den Autoren den Untertitel "ein mathematisches Abenteuer" für zentrale Informatikthemen verzeihen und das Buch kaufen, lesen und auch verschenken." Prof. Ingo Wegener in Informatik SpektrumTable of ContentsDer erste Kontakt.- Routenplanung, was ist das?.- Gestatten, Graph.- Gewicht ist Pflicht.- Eine ungefährliche Explosion.- Kurzstrecke oder nicht? Das ist hier die Frage!.- Lokal entscheiden, global optimieren.- Am Anfang war der Input.- Negativ ist negativ.- Gute Zeiten, schlechte Zeiten.- Weibliche Intuition.- Die Arbeit vor der Arbeit.- Bäumchen wechsle dich.- Prim, ohne Zahlen.- Nimm, was du kriegen kannst.- Arbor-was?.- Studieren geht über flanieren.- Spannung ohne Strom.- Eulersch oder nicht, was für ein Gedicht.- Euler und der Nikolaus.- Heute flaniert die Müllabfuhr.- Paarungszeit.- Post aus China.- Schach-Matt?.- Platonische Liebe?.- Notorisch Problematisch.- Not eines Handlungsreisenden.- Weniger ist mehr.- 150-prozentig.- Bonsai.- Gar nicht so platonisch.- Der Erfolg des Handlungsreisenden.

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Book SynopsisAufbauend auf Vorlesungen an den Universitäten Hamburg und Trier stellen die Autoren die „Theorie und Numerik restringierter Optimierungsaufgaben" umfassend dar. Ausführlich behandelt werden lineare Programme, Simplex-Verfahren und Innere-Punkte-Methoden, Optimalitätsbedingungen, nichtlineare restringierte Programme, nichtglatte Optimierung sowie Variationsungleichungen. Mit ca. 140 Aufgaben unterschiedlichen Schwierigkeitsgrades.Trade ReviewIch habe das Buch mit großem Interesse gelesen. Es enthält alle für Vorlesungen auf diesem Gebiet der nichtlinearen endlichdimensionalen Optimierung notwendigen Aussagen. Ausgehend von ihm können die Gebiete der linearen Optimierung, der Theorie nichtlinearer Optimierungsaufgaben, der Numerik nichtlinearer Optimierung und der Variationsaufgaben studiert werden. Es unterscheidet sich positiv von vielen weiteren auf dem Markt befindlichen Lehrbüchern dadurch, dass es sowohl eine umfangreiche Diskussion von Lösungsalgorithmen für Optimierungsaufgaben als auch die theoretischen Aussagen zu Optimalitäts- und Regularitätsbedingungen in hinreichender Breite und Tiefe enthält. Die Aussagen sind durchweg bewiesen, was für Vorlesungen für mathematische Studiengänge notwendig ist. Hervorheben möchte ich auch die Aufnahme von Übungsaufgaben. Zusammenfassend kann ich sagen: Das Buch ist das beste Lehrbuch zu Theorie und Lösungsverfahren der mathematischen Optimierung. Ich kann es sowohl Studierenden (mathematischer und auch anderer) Fachrichtungen als auch den Lehrenden auf dem Gebiet der mathematischen Optimierung sehr empfehlen. Anwendern von Optimierungsmethoden zum Beispiel im Operations Research wird dieses Buch ebenfalls ein wertvolles Nachschlagewerk sein. Prof. Dr. Stephan Dempe, TU Bergakademie Freiberg.Table of Contents1. Einführung.- 2. Optimalitätsbedingungen.- 3. Lineare Programme.- 4. Innere—Punkte—Methoden.- 5. Nichtlineare Optimierung.- 6. Nichtglatte Optimierung.- 7. Variationsungleichungen.

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Book SynopsisThis book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines and in particular from Economics and Social Sciences. The first part develops the fundamental aspects of mathematical modeling, dealing with both continuous time systems (differential equations) and discrete time systems (difference equations). Particular attention is devoted to equilibria, their classification in the linear case, and their stability. An effort has been made to convey intuition and emphasize connections and concrete aspects, without giving up the necessary theoretical tools. The second part introduces the basic concepts and techniques of Dynamic Optimization, covering the first elements of Calculus of Variations, the variational formulation of the most common problems in deterministic Optimal Control, both in continuous and discrete versions.

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