Optimization Books

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

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

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

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

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

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

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

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

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

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

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

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

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

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Book SynopsisThis book covers an introduction to convex optimization, one of the powerful and tractable optimization problems that can be efficiently solved on a computer. The goal of the book is tohelp develop a sense of what convex optimization is, and how it can be used in a widening array of practical contexts with a particular emphasis on machine learning.The first part of the book covers core concepts of convex sets, convex functions, and related basic definitions that serve understanding convex optimization and its corresponding models. The second part deals with one very useful theory, called duality, which enables us to: (1) gain algorithmic insights; and (2) obtain an approximate solution to non-convex optimization problems which are often difficult to solve. The last part focuses on modern applications in machine learning and deep learning.A defining feature of this book is that it succinctly relates the “story” of how convex optimization plays a role, via historical examples and trending machine learning applications. Another key feature is that it includes programming implementation of a variety of machine learning algorithms inspired by optimization fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python, CVXPY, and TensorFlow. This book does not follow a traditional textbook-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent themes and concepts. It serves as a textbook mainly for a senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in linear algebra, some exposure to probability, and basic familiarity with Python.Trade ReviewThe topic is surely still of great interest, since courses on Convex Optimization, in conjunction or not with Machine Learning applications, are ubiquitous in Engineering curricula around the world. What appears as somewhat novel here is the juxtaposition of Part I and II on convex optimization and duality with Part III on machine learning applications. The emphasis on Python, TensorFlow etc. is also practically very important and surely appreciated by the students, especially if presented via challenging practical problems. More than completeness, I believe that what is important is that the book gives a meaningful “cut” through these topics, as this books appears to do. It seems important that the author tries to motivate and link together as much as possible part III with the previous parts, explaining why part I and II are important for part III, but also highlighting what the limits of convex models are and at which point they need be superseded by more general models. Giuseppe Carlo Calafiore, Professor at the Politecnico di Torino, Italy, and visiting Professor at UC Berkeley -- Giuseppe Carlo CalafioreI have looked at the manuscript and my impression is positive, the aims and scope are actual and comprehensive. The intended audience is senior undergraduates and early graduate, which differs the book significantly from several competing books , and this should be an advantage. I would say that a good senior undergraduate level textbook on convex optimization would, in my opinion, be very timely. Arkadi Nemirovski, Georgia Tech, USA -- Arkadi NemirovskiTable of Contents Preface 1 Convex Optimization Basics 1.1 Overview of the book 1.2 Definition of convex optimization 1.3 Tractability of convex optimization and gradient descent 1.4 Linear Program 1.5 Least Squares 1.6 Test error, regularization and CVXPY implementation 1.7 Computed tomography 1.8 Quadratic program 1.9 Second-order cone program 1.10 Semi-definite program 1.11 SDP relaxation 1.12 Problem Sets 2 Duality 2.1 Strong duality 2.2 Interior point method 2.3 Proof of strong duality theorem 2.4 Weak duality 2.5 Lagrange relaxation for Boolean problems 2.6 Lagrange relaxation for the MAXCUT problem 2.7 Problem Sets 3 Machine Learning Applications 3.1 Supervised learning and optimization 3.2 Logistic regression 3.3 Deep learning 3.4 Deep learning II 3.5 DL: TensorFlow implementation 3.6 Unsupervised Learning: Generative modeling 3.7 Generative Adversarial Networks (GANs) 3.8 GANs: TensorFlow implementation 3.9 Wasserstein GAN 3.10 Wasserstein GAN II 3.11 Wasserstein GAN: TensorFlow implementation 3.12 Fair machine learning 3.13 A fair classifier and its connection to GANs 3.14 A fair classifier: TensorFlow implementation Appendices

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Book SynopsisOptimization should be the science of making the best possible decisions. Making decisions is a virtually universal human activity encountered by professionals (in any field) or people in their everyday lives. You would think, then, that the study of making good decisions is a subject that should be taught broadly to students throughout engineering, the physical and social sciences, business, and policy. Yet today, “optimization” is widely taught as a mathematically sophisticated subject, often limited to graduate students in specialized fields.In operations research (or industrial engineering), “optimization” is equivalent to deterministic math programming, starting with linear programs (and the simplex algorithm), and then transitioning through integer linear programs and nonlinear programs. If you are in departments like electrical or mechanical engineering, optimization means teaching optimal control. And if you are in computer science, optimization today could be interpreted in the context of machine learning (such as fitting models to data) or as reinforcement learning.This book claims that the traditional style of teaching optimization is misguided and out of date. First, while the simplex algorithm is a powerful strategy for solving linear programs, the details of the simplex algorithm are completely inappropriate in an introductory course in optimization. Second, while linear programs are appropriate for solving many problems, they are only applicable to a tiny fraction of all decisions. Third, linear programs (along with integer and nonlinear programs) are static models for problems with (typically) vector-valued decisions. By contrast, most decisions are sequential since they are made periodically over time as new information is arriving. In addition, the vast majority of these decisions are scalar (possibly continuous or discrete).This book is designed for instructors (or potential instructors) looking to introduce the science of making good decisions to the broadest possible audience. It should also be of interest to anyone who has already had a traditional course in optimization of any type. The presentation is organized around a series of topics that suggest a fundamentally different approach to teaching “optimization” spanning both sequential decision problems (which offer the simplest problem settings) before transitioning to more complex vector-valued decisions. It also makes the case that most problems which are modeled as linear (or integer, or nonlinear programs) are actually methods for making decisions in a sequential setting. For this reason, these topics are introduced with much less emphasis on algorithms than is traditionally used, both in static and sequential settings.

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Book SynopsisThis book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance. Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites. The topology optimization proposed has significantly increased the fracture resistance of the composites studied.Table of ContentsIntroduction ix Part 1. Multiscale Topology Optimization in the Context of Non-separated Scales 1 Chapter 1. Size Effect Analysis in Topology Optimization for Periodic Structures Using the Classical Homogenization 3 1.1. The classical homogenization method 4 1.1.1. Localization problem 4 1.1.2. Definition and computation of the effective material properties 7 1.1.3. Numerical implementation for the local problem with PER 9 1.2. Topology optimization model and procedure 10 1.2.1. Optimization model and sensitivity number 10 1.2.2. Finite element meshes and relocalization scheme 12 1.2.3. Optimization procedure 14 1.3. Numerical examples 16 1.3.1. Doubly clamped elastic domain 17 1.3.2. L-shaped structure 19 1.3.3. MBB beam 24 1.4. Concluding remarks 25 Chapter 2. Multiscale Topology Optimization of Periodic Structures Taking into Account Strain Gradient 29 2.1. Non-local filter-based homogenization for non-separated scales 30 2.1.1. Definition of local and mesoscopic fields through the filter 30 2.1.2. Microscopic unit cell calculations 33 2.1.3. Mesoscopic structure calculations 39 2.2. Topology optimization procedure 41 2.2.1. Model definition and sensitivity numbers 41 2.2.2. Overall optimization procedure 42 2.3. Validation of the non-local homogenization approach 43 2.4. Numerical examples 45 2.4.1. Cantilever beam with a concentrated load 46 2.4.2. Four-point bending lattice structure 52 2.5. Concluding remarks 55 Chapter 3. Topology Optimization of Meso-structures with Fixed Periodic Microstructures 57 3.1. Optimization model and procedure 58 3.2. Numerical examples 61 3.2.1. A double-clamped beam 61 3.2.2. A cantilever beam 64 3.3. Concluding remarks 66 Part 2. Topology Optimization for Maximizing the Fracture Resistance 67 Chapter 4. Topology Optimization for Optimal Fracture Resistance of Quasi-brittle Composites 69 4.1. Phase field modeling of crack propagation 71 4.1.1. Phase field approximation of cracks 71 4.1.2. Thermodynamics of the phase field crack evolution 72 4.1.3. Weak forms of displacement and phase field problems 75 4.1.4. Finite element discretization 76 4.2. Topology optimization model for fracture resistance 78 4.2.1. Model definitions 78 4.2.2. Sensitivity analysis 80 4.2.3. Extended BESO method 85 4.3. Numerical examples 87 4.3.1. Design of a 2D reinforced plate with one pre-existing crack notch 88 4.3.2. Design of a 2D reinforced plate with two pre-existing crack notches 93 4.3.3. Design of a 2D reinforced plate with multiple pre-existing cracks 96 4.3.4. Design of a 3D reinforced plate with a single pre-existing crack notch surface 98 4.4. Concluding remarks 101 Chapter 5. Topology Optimization for Optimal Fracture Resistance Taking into Account Interfacial Damage 103 5.1. Phase field modeling of bulk crack and cohesive interfaces 104 5.1.1. Regularized representation of a discontinuous field 104 5.1.2. Energy functional 106 5.1.3. Displacement and phase field problems 108 5.1.4. Finite element discretization and numerical implementation 111 5.2. Topology optimization method 114 5.2.1. Model definitions 114 5.2.2. Sensitivity analysis 116 5.3. Numerical examples 119 5.3.1. Design of a plate with one initial crack under traction 120 5.3.2. Design of a plate without initial cracks for traction loads 123 5.3.3. Design of a square plate without initial cracks in tensile loading 125 5.3.4. Design of a plate with a single initial crack under three-point bending 128 5.3.5. Design of a plate containing multiple inclusions 130 5.4. Concluding remarks 133 Chapter 6. Topology Optimization for Maximizing the Fracture Resistance of Periodic Composites 135 6.1. Topology optimization model 136 6.2. Numerical examples 138 6.2.1. Design of a periodic composite under three-point bending 138 6.2.2. Design of a periodic composite under non-symmetric three-point bending 146 6.3. Concluding remarks 151 Conclusion 153 References 157 Index 173

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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. “Applications of Combinatorial Optimization” is presenting a certain number among the most common and well-known applications of Combinatorial Optimization.Table of ContentsPreface xiii Chapter 1. Airline Crew Pairing Optimization 1 Laurent ALFANDARI and Anass NAGIH 1.1. Introduction 1 1.2. Definition of the problem 2 1.3. Solution approaches 7 1.4. Solving the subproblem for column generation 11 1.5. Conclusion 21 1.6. Bibliography 22 Chapter 2. The Task Allocation Problem 23 Moaiz BEN DHAOU and Didier FAYARD 2.1. Presentation 24 2.2. Definitions and modeling 24 2.3. Review of the main works 29 2.4. A little-studied model 38 2.5. Conclusion 43 2.6. Bibliography 43 Chapter 3. A Comparison of Some Valid Inequality Generation Methods for General 0–1 Problems 49 Pierre BONAMI and Michel MINOUX 3.1. Introduction 49 3.2. Presentation of the various techniques tested 53 3.3. Computational results 67 3.4. Bibliography 70 Chapter 4. Production Planning 73 Nadia BRAUNER, Gerd FINKE and Maurice QUEYRANNE 4.1. Introduction 73 4.2. Hierarchical planning 74 4.3. Strategic planning and productive system design 75 4.4. Tactical planning and inventory management 77 4.5. Operations planning and scheduling 90 4.6. Conclusion and perspectives 104 4.7. Bibliography 105 Chapter 5. Operations Research and Goods Transportation 111 Teodor Gabriel CRAINIC and Frédéric SEMET 5.1. Introduction 111 5.2. Goods transport systems 113 5.3. Systems design 115 5.4. Long-distance transport 122 5.5. Vehicle routing problems 137 5.6. Exact models and methods for the VRP 139 5.7. Heuristic methods for the VRP 147 5.8. Conclusion 160 5.9. Appendix: metaheuristics 161 5.10. Bibliography 164 Chapter 6. Optimization Models for Transportation Systems Planning 177 Teodor Gabriel CRAINIC and Michael FLORIAN 6.1. Introduction 177 6.2. Spatial interaction models 178 6.3. Traffic assignment models and methods 181 6.4. Transit route choice models 193 6.5. Strategic planning of multimodal systems 197 6.6. Conclusion 204 6.7. Bibliography 204 Chapter 7. A Model for the Design of a Minimum-cost Telecommunications Network 209 Marc DEMANGE, Cécile MURAT, Vangelis Th. PASCHOS and Sophie TOULOUSE 7.1. Introduction 209 7.2. Minimum cost network construction 210 7.3. Mathematical model, general context 213 7.4. Proposed algorithm 216 7.5. Critical points 220 7.6. Conclusion 223 7.7. Bibliography 223 Chapter 8. Parallel Combinatorial Optimization 225 Van-Dat CUNG, Bertrand LE CUN and Catherine ROUCAIROL 8.1. Impact of parallelism in combinatorial optimization 225 8.2. Parallel metaheuristics 226 8.3. Parallelizing tree exploration in exact methods 235 8.4. Conclusion 247 8.5. Bibliography 248 Chapter 9. Network Design Problems: Fundamental Methods 253 Alain Quilliot 9.1. Introduction 253 9.2. The main mathematical and algorithmic tools for network design 258 9.3. Models and problems 275 9.4. The STEINER-EXTENDED problem 280 9.5. Conclusion 281 9.6 Bibliography 281 Chapter 10. Network Design Problems: Models and Applications 291 Alain Quilliot 10.1. Introduction 291 10.2. Models and location problems 293 10.3. Routing models for telecommunications 298 10.4. The design or dimensioning problem in telecommunications 301 10.5. Coupled flows and multiflows for transport and production 306 10.6. A mixed network pricing model 314 10.7. Conclusion 319 10.8. Bibliography 319 Chapter 11. Multicriteria Task Allocation to Heterogenous Processors with Capacity and Mutual Exclusion Constraints 327 Bernard ROY and Roman SLOWINSKI 11.1. Introduction and formulation of the problem 328 11.2. Modeling the set of feasible assignments 331 11.3. The concept of a blocking configuration and analysis of the unblocking means 334 11.4. The multicriteria assignment problem 346 11.5. Exploring a set of feasible non-dominated assignments in the plane g2 × g3 348 11.6. Numerical example 357 11.7. Conclusion 363 11.8. Bibliography 364 List of Authors 365 Index 369 Summary of Other Volumes in the Series 373

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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 aim 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, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting 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 Combinatioral Optimization Problems 1 Chapter 1 Basic Concepts in Algorithms and Complexity Theory 3 Vangelis Th. Paschos Chapter 2 Randomized Complexity 21 Jérémy Barbay Part II Classic Solution Methods 39 Chapter 3 Branch-and-Bound Methods 41 Irène Charon and Olivier Hudry Chapter 4 Dynamic Programming 71 Bruno Escoffier and Olivier Spanjaard Part III Elements from Mathematical Programming 101 Chapter 5 Mixed Integer Linear Programming Models for Combinatorial Optimization Problems 103 Frédérico Della Croce Chapter 6 Simplex Algorithms for Linear Programming 135 Frédérico Della Croce and Andrea Grosso Chapter 7 A Survey of Some Linear Programming Methods 157 Pierre Tolla Chapter 8 Quadratic Optimization in 0-1 Variables 189 Alain Billionnet Chapter 9 Column Generation in Integar Linear Programming 235 Irène Loiseau, Alberto Ceselli, Nelson Maculan and Matteo Salani Chapter 10 Polyhedral Approaches 261 Ali Ridha Mahjoub Chapter 11 Constaint Programming 325 Claude Le Pape General Bibliography 339 List of Authors 363 Index 367 Summary of Other Volumes in the Series 371

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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 aim 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, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.Table of ContentsPreface xiii Chapter 1 Airline Crew Pairing Optimization 1 Laurent Alfandari and Anass Nagih Chapter 2 The Task Allocation Problem 23 Moaiz Ben Dhaou and Didier Fayard Chapter 3 A Comparison of Some Valid Inequality Generation Methods for General 0-1 Problems 49 Pierre Bonami and Michel Minoux Chapter 4 Production Planning 73 Nadia Brauner, Gerd Finke and Maurice Queyranne Chapter 5 Operations Research and Goods Transportation 111 Teodor Gabriel Crainic and Frédéric Semet Chapter 6 Optimization Models for Transportation Systems Planning 177 Teodor Gabriel Crainic and Michael Florian Chapter 7 A Model for the Design of a Minimum-cost Telecomminications Network 209 Marc Demange, Cécile Murat, Vangelis Th. Paschos and Sophie Toulouse Chapter 8 Parallel Combinatorial Optimization 225 Van-Dat Cung, Bertrand Le Cun and Catherine Roucairol Chapter 9 Network Design Problems: Fundamental Methods 253 Alain Quilliot Chapter 10 Network Design Problems: Models and Applications 291 Alain Quilliot Chapter 11 Multicriteria Task Allocation to Heterogenous Processors with Capacity and Mutual Exclusion Constraints 327 Bernard Roy and Roman Slowinski General Bibliography 365 List of Authors 401 Index 405 Summary of Other Volumes in the Series 409

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Book SynopsisEvolutionary computation algorithms are employed to minimize functions with large number of variables. Biogeography-based optimization (BBO) is an optimization algorithm that is based on the science of biogeography, which researches the migration patterns of species. These migration paradigms provide the main logic behind BBO. Due to the cross-disciplinary nature of the optimization problems, there is a need to develop multiple approaches to tackle them and to study the theoretical reasoning behind their performance. This book explains the mathematical model of BBO algorithm and its variants created to cope with continuous domain problems (with and without constraints) and combinatorial problems.Table of ContentsChapter 1 The Science of Biogeography 1 1.1 Introduction 1 1.2 Island biogeography 3 1.3 Influence factors for biogeography 6 Chapter 2 Biogeography and Biological Optimization 11 2.1 A mathematical model of biogeography 11 2.2 Biogeography as an optimization process 16 2.3 Biological optimization 19 2.3.1 Genetic algorithms 19 2.3.2 Evolution strategies 20 2.3.3 Particle swarm optimization 21 2.3.4 Artificial bee colony algorithm 22 2.4 Conclusion 23 Chapter 3 A Basic BBO Algorithm 25 3.1 BBO definitions and algorithm 25 3.1.1 Migration 26 3.1.2 Mutation 27 3.1.3 BBO implementation 27 3.2 Differences between BBO and other optimization algorithms 35 3.2.1 BBO and genetic algorithms 35 3.2.2 BBO and other algorithms 36 3.3 Simulations 37 3.4 Conclusion 44 Chapter 4 BBO Extensions 45 4.1 Migration curves 45 4.2 Blended migration 49 4.3 Other approaches to BBO 51 4.4 Applications 56 4.5 Conclusion 59 Chapter 5 BBO as a Markov Process 61 5.1 Markov definitions and notations 61 5.2 Markov model of BBO 72 5.3 BBO convergence 79 5.4 Markov models of BBO extensions 90 5.5 Conclusions 99 Chapter 6 Dynamic System Models of BBO 103 6.1 Basic notation 103 6.2 Dynamic system models of BBO 105 6.3 Applications to benchmark problems 119 6.4 Conclusions 122 Chapter 7 Statistical Mechanics Approximations of BBO 123 7.1 Preliminary foundation 123 7.2 Statistical mechanics model of BBO 128 7.2.1 Migration 128 7.2.2 Mutation 134 7.3 Further discussion 141 7.3.1 Finite population effects 141 7.3.2 Separable fitness functions 142 7.4 Conclusions 143 Chapter 8 BBO for Combinatorial Optimization 145 8.1 Traveling salesman problem 147 8.2 BBO for the TSP 148 8.2.1 Population initialization 148 8.2.2 Migration in the TSP 150 8.2.3 Mutation in the TSP 157 8.2.4 Implementation framework 159 8.3 Graph coloring 163 8.4 Knapsack problem 165 8.5 Conclusion 167 Chapter 9 Constrained BBO 169 9.1 Constrained optimization 170 9.2 Constraint-handling methods 172 9.2.1 Static penalty methods 172 9.2.2 Superiority of feasible points 173 9.2.3 The eclectic evolutionary algorithm 174 9.2.4 Dynamic penalty methods 174 9.2.5 Adaptive penalty methods 176 9.2.6 The niched-penalty approach 177 9.2.7 Stochastic ranking 178 9.2.8 ε-level comparisons 178 9.3 BBO for constrained optimization 179 9.4 Conclusion 185 Chapter 10 BBO in Noisy Environments 187 10.1 Noisy fitness functions 188 10.2 Influence of noise on BBO 190 10.3 BBO with re-sampling 193 10.4 The Kalman BBO 196 10.5 Experimental results 199 10.6 Conclusion 201 Chapter 11 Multi-objective BBO 203 11.1 Multi-objective optimization problems 204 11.2 Multi-objective BBO 211 11.2.1 Vector evaluated BBO 211 11.2.2 Non-dominated sorting BBO 213 11.2.3 Niched Pareto BBO 216 11.2.4 Strength Pareto BBO 218 11.3 Real-world applications 223 11.3.1 Warehouse scheduling model 223 11.3.2 Optimization of warehouse scheduling 229 11.4 Conclusion 231 Chapter 12 Hybrid BBO Algorithms 233 12.1 Opposition-based BBO 234 12.1.1 Opposition definitions and concepts 234 12.1.2 Oppositional BBO 236 12.1.3 Experimental results 238 12.2 BBO with local search 240 12.2.1 Local search methods 240 12.2.2 Simulation results 245 12.3 BBO with other EAs 247 12.3.1 Iteration-level hybridization 247 12.3.2 Algorithm-level hybridization 250 12.3.3 Experimental results 254 12.4 Conclusion 256 Appendices 259 Appendix A Unconstrained Benchmark Functions 261 Appendix B Constrained Benchmark Functions 265 Appendix C Multi-objective Benchmark Functions 289 Bibliography 309 Index 325

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Book SynopsisThis is the first book devoted entirely to Particle Swarm Optimization (PSO), which is a non-specific algorithm, similar to evolutionary algorithms, such as taboo search and ant colonies. Since its original development in 1995, PSO has mainly been applied to continuous-discrete heterogeneous strongly non-linear numerical optimization and it is thus used almost everywhere in the world. Its convergence rate also makes it a preferred tool in dynamic optimization.Table of ContentsForeword. Introduction. Part 1: Particle Swarm Optimization. Chapter 1. What is a difficult problem? Chapter 2. On a table corner. Chapter 3. First formulations. Chapter 4. Benchmark set. Chapter 5. Mistrusting chance. Chapter 6. First results. Chapter 7. Swarm: memory and influence graphs. Chapter 8. Distributions of proximity. Chapter 9. Optimal parameter settings. Chapter 10. Adaptations. Chapter 11. TRIBES or co-operation of tribes. Chapter 12. On the constraints. Chapter 13. Problems and applications. Chapter 14. Conclusion. Part 2: Outlines. Chapter 15. On parallelism. Chapter 16. Combinatorial problems. Chapter 17. Dynamics of a swarm. Chapter 18. Techniques and alternatives. Further Information. Bibliography. Index.

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Book SynopsisThis book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games.The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general.Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.Trade Review“This book is a great resource for graduate students and those who want to learn and understand stochastic control theory. It is also a great read for experts who want to gain a broader overview of the subject and wish to see connections between different techniques. … this is an excellent book and a great complement to the current offering in stochastic control.” (Jan Palczewski, SIAM Review, Vol. 62 (1), 2020)Table of ContentsIntroduction.- State Representation of Linear Dynamical Systems.- Optimal Control of Linear Dynamical Systems.- Estimation Theory.- Further Techniques of Estimation.- Compliments on Probability Theory.- Filtering Theory in Continuous Time.- Stochastic Control of Linear Dynamic Systems with Full Information.- Stochastic Control of Linear Dynamical Systems with Partial Information.- Deterministic Optimal Control.- Stochastic Optimal Control.- Additional Results for BSDE.- Stochastic Control Problems in Finance.- Stochastic Control for Non-Markov Processes.- Principal Agent Control Problems.- Differential Games.- Stackelberg Differential Games.- Target Problems.

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Book SynopsisThis volume provides resourceful thinking and insightful management solutions to the many challenges that decision makers face in their predictions, preparations, and implementations of the key elements that our societies and industries need to take as they move toward digitalization and smartness. The discussions within the book aim to uncover the sources of large-scale problems in socio-industrial dilemmas, and the theories that can support these challenges. How theories might also transition to real applications is another question that this book aims to uncover. In answer to the viewpoints expressed by several practitioners and academicians, this book aims to provide both a learning platform which spotlights open questions with related case studies. The relationship between Industry 4.0 and Society 5.0 provides the basis for the expert contributions in this book, highlighting the uses of analytical methods such as mathematical optimization, heuristic methods, decomposition methods, stochastic optimization, and more. The book will prove useful to researchers, students, and engineers in different domains who encounter large scale optimization problems and will encourage them to undertake research in this timely and practical field. The book splits into two parts. The first part covers a general perspective and challenges in a smart society and in industry. The second part covers several case studies and solutions from the operations research perspective for large scale challenges specific to various industry and society related phenomena.Table of ContentsPart 1.- Risk Based Optimization of Integrated Fabrication/Fulfillment Supply Chains (Nasim Nezamoddini, Faisal Aqlan, Amirhosein Gholami).- μθ-EGF: A New Multi-Thread Implementation Algorithm for the Packing Problem inspired by Electromagnetic Fields and Gravitational Effects (Felix Martinez-Rios and Jose Antonio Marmolejo-Saucedo).- The Vector Optimization Method for Solving Integer Linear Programming Problems. Application for the Unit Commitment Problem in Electrical Power Production (Lenar Nizamov).- An Outer Approximation Algorithm for Capacitated Disassembly Scheduling Problem with Parts Commonality and Random Demand (Kanglin Liu, MengWang, Zhi-Hai Zhang),- Multi-Tree Decomposition Methods for Large-Scale Mixed Integer Nonlinear Optimization (Ivo Nowak, Pavlo Muts, and Eligius M.T. Hendrix).- An Embarrassingly Parallel Method for Large-Scale Stochastic Programs (Burhaneddin Sandıkçı and Osman Y. Özaltın).- Part 2.- How to Effectively Train Large Scale Machines (Avan Samareh, Mahshid Salemi Parizi).- A Graph Search Algorithm for Solving Large Scale Median Problems on Real Road Networks (Saeed Ghanbartehrania, J. David Porterb, Mahnoush Samadi Dinania).- Solving Large Scale Optimization Problems in the Transportation Industry and Beyond through Column Generation (Yanqi Xu).- Dynamic Energy Management (Nicholas Moehle, Enzo Busseti, Stephen Boyd, and Matt Wytock).- An Approximation-Based Approach for Chance-Constrained Vehicle Routing and Air Traffic Control Problems (Lijian Chen).- Algorithmic Mechanism Design for Collaboration in Large-scale Transportation Networks (Minghui Lai and Xiaoqiang Cai).- Kantorovich-Rubinstein Distance Minimization: Application to Location Problems (Viktor Kuzmenko, Stan Uryasev).

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Book SynopsisThis book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20–24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.Table of Contents- Poincaré and Hardy Inequalities on Homogeneous Trees. - Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass. - Optimization of the Structural Performance of Non-homogeneous Partially Hinged Rectangular Plates. - Energy-Like Functional in a Quasilinear Parabolic Chemotaxis System. - Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance. - Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains. - Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition. - Neutral Inclusions, Weakly Neutral Inclusions, and an Over-determined Problem for Confocal Ellipsoids. - Nonexistence of Radial Optimal Functions for the Sobolev Inequality on Cartan-Hadamard Manifolds. - Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games. - An Interpolating Inequality for Solutions of Uniformly Elliptic Equations. - Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method. - A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient. - Remark on One Dimensional Semilinear DampedWave Equation in a CriticalWeighted L2-space.

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Book SynopsisThis book dives into radio resource allocation optimizations, a research area for wireless communications, in a pragmatic way and not only includes wireless channel conditions but also incorporates the channel in a simple and practical fashion via well-understood equations. Most importantly, the book presents a practical perspective by modeling channel conditions using terrain-aware propagation which narrows the gap between purely theoretical work and that of industry methods. The provided propagation modeling reflects industry grade scenarios for radio environment map and hence makes the channel based resource allocation presented in the book a field-grade view. Also, the book provides large scale simulations that account for realistic locations with terrain conditions that can produce realistic scenarios applicable in the field. Most portions of the book are accompanied with MATLAB code and occasionally MATLAB/Python/C code. The book is intended for graduate students, academics, researchers of resource allocation in mathematics, computer science, and electrical engineering departments as well as working professionals/engineers in wireless industry.Table of ContentsIntroduction.- Utility Functions and Resource Allocation.- Resource Allocation without Channel.- Distributed or Centralized.- Channel Conditions and Resource Allocation.- Propagation Modeling .- Simulation.- Conclusion.

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Book SynopsisThis richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysis would be helpful but is not prerequisite. Trade Review“In the reviewer's opinion, this is an important book … . a lot of applications are given, so on one hand the readers can benefit from deep insights into the mathematical background of optimization theory … . This book, which as all books reflects the tastes of its authors, is a solid reference, not only for graduate students and postgraduate students, but also for all those researchers interested in recent developments of optimization theory and methods.” (Giorgio Giorgi, Mathematical Reviews, December, 2022)Table of ContentsPrelude.- Convex optimization.- Optimization under uncertainty.- Minimization problems.- Perturbation and duality.- Without convexity or smoothness.- Generalized Equations.- Risk modeling and sample averages.- Games and minsup problems.- Decomposition.

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Book SynopsisThis book presents techniques for determining uncertainties in numerical solutions with applications in the fields of business administration, civil engineering, and economics, using Excel as a computational tool. Also included are solutions to uncertainty problems involving stochastic methods. The list of topics specially covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi objective optimization, and Game Theory, as well as linear algebraic equations, and probability and statistics. The book also provides a selection of numerical methods developed for Excel, in order to enhance readers’ understanding. As such, it offers a valuable guide for all graduate and undergraduate students in the fields of economics, business administration, civil engineering, and others that rely on Excel as a research tool.Table of ContentsChapter 1: Some tips to use EXCEL.- Chapter 2: Some useful Numerical Methods.- Chapter 3: Probabilities with EXCEL.- Chapter 4: Stochastic Processes.- Chapter 5: Representation of Random Variables.- Chapter 6: Uncertain Algebraic Equations.- Chapter 7: Random Differential Equations.- Chapter 8: UQ in Game Theory.- Chapter 9: Optimization under uncertainty.- Chapter 10: Reliability.- Bibliography.- Index.

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Book SynopsisThis book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.Table of ContentsTheory of the mesh methods for the boundary-value problems in Mathematical Physics.- Non-linear mathematical models in mechanics and physics.- Algorithms for solving variational inequalities.- Computing Science and educational systems.

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Book SynopsisThis revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.Table of ContentsMechanics of Systems of Particles .- Mathematical Preliminaries.- Mechanics of Continuous Media.- Motions and Comparison Motions of a Mixture.- Singular Surfaces.- Index.

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Book SynopsisIn this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.Table of Contents-Preface.- Introduction.- List of symbols and abbreviations.- 1. Elements of the computing theory.- 2. Theories of computational complexity.- 3. Interlination of functions.- 4. Interflatation of functions.- 5. Cubature formulae using interlanation functions.- 6. Testing the quality of algorithm programs.- 7. Computer technologies of solving problems of computational and applied mathematics with fixed values of quality characteristics.- Bilbiography.- Index.- About the Authors.

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Book SynopsisThis book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science.“Mathematicians have never been comfortable handling infinities… But an entirely new type of mathematics looks set to by-pass the problem… Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem… ”MIT Technology Review“These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing.“I am sure that the new approach … will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science.“Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing.“The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort.” P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft ComputingTrade Review“This book could have deep impact upon not only local, global, multi-objective optimization and machine learning, but also possibly on applied mathematics more broadly and numerical computation. People interested in new ideas for computer science and its foundations and possibly even the philosophy of mathematics will find this volume interesting, as would those working in theoretical or applied optimization.” (Jonathan Gillard, Optimization Letters, Vol. 17 (2), 2023)Table of ContentsA New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals.- Nonlinear Optimization: A Brief Overview.- The role of grossone in Nonlinear Programming and Exact Penalty Methods.

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Book SynopsisThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.Trade Review“Each chapter ends with an exercise section … . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.” (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)“This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 2023)“Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. … The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis … . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors … .” (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)Table of ContentsFundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.

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Book SynopsisThis book pursues the ambitious goal of combining floating wind turbine design optimization and reliability assessment, which has in fact not been done before. The topic is organized into a series of very ambitious objectives, which start with an initial state-of-the-art review, followed by the development of high-fidelity frameworks for a disruptive way to design next generation floating offshore wind turbine (FOWT) support structures. The development of a verified aero-hydro-servo-elastic coupled numerical model of dynamics for FOWTs and a holistic framework for automated simulation and optimization of FOWT systems, which is later used for the coupling of design optimization with reliability assessment of FOWT systems in a computationally and time-efficient manner, has been an aim of many groups internationally towards implementing a performance-based/goal-setting approach in the design of complex engineering systems. The outcomes of this work quantify the benefits of an optimal design with a lower mass while fulfilling design constraints. Illustrating that comprehensive design methods can be combined with reliability analysis and optimization algorithms towards an integrated reliability-based design optimization (RBDO) can benefit not only the offshore wind energy industry but also other applications such as, among others, civil infrastructure, aerospace, and automotive engineering.Table of ContentsIntroduction.- Review of Reliability-Based Risk Analysis Methods Used in the Offshore Wind Industry.- Floating Offshore Wind Turbine Systems.- Modeling, Automated Simulation, and Optimization.- Design Optimization of FloatingWind Turbine Support Structures.- Reliability-Based Design Optimization of a Spar-Type FloatingWind Turbine Support Structure.- Discussion.- Conclusions.

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Book SynopsisThis volume is addressed to people who are interested in modern mathematical solutions for real life applications. In particular, mathematical modeling, simulation and optimization is nowadays successfully used in various fields of application, like the energy- or health-sector. Here, mathematics is often the driving force for new innovations and most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.Table of ContentsPart I Prognostic MR Thermometry for Thermal Ablation of Liver Tumours.- 1 Sebastian Blauth et al., Mathematical Modeling and Simulation of Laser-Induced Thermotherapy for the Treatment of Liver Tumors.- 2 Matthias Andres and René Pinnau, The Cattaneo Model for Laser-Induced Thermotherapy: Identification of the Blood-Perfusion Rate.- 3 Kevin Tolle and Nicole Marheineke, On Online Parameter Identification in Laser-Induced Thermotherapy.- Part II Energy-efficient High Temperature Processes via Shape Optimisation.- 4 Robert Feßler at al., Feasibility Study on Simulating a 3D Furnace Including the Effects of Reactions and Vaporization.- 5 Thomas Marx et al., Shape Optimization for the SP1–Model for Convective Radiative Heat Transfer- 6 Nicolas Dietrich et al., Diffusive Radiation Models for Optimal Shape Design in Phosphate Production.- 7 Ruben Sanchez at al., Adjoint-based sensitivity analysis in high-temperature fluid flows with participating media.

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Book SynopsisThis text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material.Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.Table of Contents1. Introduction.- 2. Controllability problem.- 3. Optimal control problem.- 4. Solution to optimal control problems.- 5. Conclusion.- A. Elliptic integrals, functions and equation of pendulum.- Bibliography and further reading.- Index.

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Book SynopsisIntroductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.Trade Review“This book introduces combinatorial optimization with a methodology-oriented organization. It targets undergraduate and graduate students and contains a good mix of theoretical results (with proof) and examples, which helps the reader acquire ideas and concepts. The chapters end with a list of exercises for the students.” (Francisco Chicano, Mathematical Reviews, January, 2024)“The book can appropriately be used as a textbook in a graduate course. All the algorithms are clearly explained and presented. It is a very valuable book for successful application of real problems from combinatorial optimization. … this book is an excellent contribution to the field of combinatorial optimization, and it is highly recommended to the students and researchers in optimization.” (Samir Kumar Neogy, zbMATH 1512.90001, 2023)Table of Contents1. Introduction.-2. Divide-and-Conquer.- 3. Dynamic Programming and Shortest Path.- 4. Greedy Algorithm and Spanning Tree.- 5. Incremental Method and Maximum Network Flow.- 6. Linear Programming.- 7. Primal-Dual Methods and Minimum Cost Flow.- 8. NP-hard Problems and Approximation Algorithms.- 9. Restriction and Steiner Tree.- 10. Greedy Approximation and Submodular Optimization.- 11. Relaxation and Rounding. 12. Nonsubmodular Optimization.- Bibliography.

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Book SynopsisThis open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content.Table of ContentsPart I: Combinatorial Optimization, Complexity Theory and Problem Modelling.- 1. Elements of Graphs and Complexity Theory.- 2. A Short List of Combinatorial Optimization Problems.- 3. Problem Modelling.- Part II: Basic Heuristic Techniques.- 4. Constructive Methods.- 5. Local Search.- 6. Decomposition Methods.- Part III: Popular Metaheuristics.- 7. Randomized Methods.- 8. Construction Learning.- 9. Local Search Learning.- 10. Population Management.- 11. Heuristics Design.- 12. Codes.

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Book SynopsisThis book gives a detailed information of various real-life applications from various fields using nature inspired optimization techniques. These techniques are proven to be efficient and robust in many difficult problems in literature. The authors provide detailed information about real-life problems and how various nature inspired optimizations are applied to solve these problems. The authors discuss techniques such as Biogeography Based Optimization, Glow Swarm Optimization, Elephant herd Optimization Algorithm, Cuckoo Search Algorithm, Ant Colony Optimization, and Grey Wolf Optimization etc. These algorithms are applied to a wide range of problems from the field of engineering, finance, medicinal etc. As an important part of the Women in Science and Engineering book series, the work highlights the contribution of women leaders in nature inspired optimization, inspiring women and men, girls and boys to enter and apply themselves to the field.Table of Contents1) AN OVERVIEW OF SWARM INTELLIGENCE BASED ALGORITHMS2) Particle Swarm Optimization and its Applications in the Manufacturing Industry3) Role of Machine Learning in Bioprocess Engineering: Current Perspectives and Future Directions 4) Advanced Selection Operation for Differential Evolution Algorithm 5) Profit Optimization of Two-Unit Briquetting System using grey wolf Optimization algorithm 6) Solving Portfolio optimization using Sine-cosine Algorithm embedded mutation operations7) Detecting Group Shilling Profiles in Recommender Systems: A Hybrid Clustering and Grey Wolf Optimizer Technique8) SINGLE IMAGE REFLECTION REMOVAL USING DEEP LEARNING 9) Social media analysis: A tool for popularity prediction using machine learning classifiers

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Book SynopsisThis book provides the current status of research on the application of OR methods to solve emerging and relevant operations management problems. Each chapter is a selected contribution of the IO2021 - XXI Congress of APDIO, the Portuguese Association of Operational Research, held in Figueira da Foz from 7 to 8 November 2021. Under the theme of analytics for a better world, the book presents interesting results and applications of OR cutting-edge methods and techniques to various real-world problems. Of particular importance are works applying nonlinear, multi-objective optimization, hybrid heuristics, multicriteria decision analysis, data envelopment analysis, simulation, clustering techniques and decision support systems, in different areas such as supply chain management, production planning and scheduling, logistics, energy, telecommunications, finance and health. All chapters were carefully reviewed by the members of the scientific program committee.Table of ContentsA. R. Aguiar, T. Ramos, M. Isabel Gomes, Chapter 1 – A Biased Random-Key Genetic Algorithm for the Home Care Routing and Scheduling Problem: exploring the algorithm's configuration process.- B. F. Azevedo, F. Alvelos, Ana Maria A. C. Rocha, T. Brito, José Lima, Ana I. Pereira, Chapter 2 – An Integer Programming Approach for Sensor Location in a Forest Fire Monitoring System.- C. Bessa, R. Duque, A. Jesus, C. Silva, L. Eberle, S. Moniz, Chapter 3 – Capacity allocation incorporating market equity concerns: a Pharmaceutical Supply Chain case study.- I. S. Costa, R. Figueiredo, C. Requejo, Chapter 4 – The Shortest Path in Signed Graphs.- M. Dias, N. Lourenço, C. Silva, S. Moniz, Chapter 5 – The Break Point: A Machine Learning Approach to Web Breaks in Paper Mills.- M. M. Lima, F. Soares de Sousa, E. G. Öztürk, P. F. Rocha, A. M. Rodrigues, J. S. Ferreira, A. C. Nunes, I. C. Lopes, C. Teles Oliveira, Chapter 6 – A resectorization of fire brigades in the north of Portugal.- L. Magalhães, J. S. Guedes, J. Freire de Sousa, Chapter 7 – A Holistic Framework for Increasing Agility in a Production Process.- P. Nascimento, C. Silva, S. Mueller, S. Moniz, Chapter 8 – Nesting and scheduling for additive manufacturing: an approach considering order due dates.- E. Göksu Öztürk, Filipe Soares de Sousa, M. M. Lima, P. F. Rocha, A. M. Rodrigues, J. S. Ferreira, A. C. Nunes, I. C. Lopes, C. Teles Oliveira, Chapter 9 – Developing a System for Sectorization: An Overview.- M. Pascoal, M. T. Godinho, A. Moghanni, Chapter 10 – New models for finding K short and dissimilar paths.- M. T. Pereira, M. Oliveira, F. A. Ferreira, A. Barreiras, L. Carneiro, Chapter 11 – Time Windows Vehicle Routing Problem to on-time transportation of biological products on healthcare centres.- H. S. Rodrigues, Artur M. C. Brito da Cruz, Chapter 12 – The role of communication on the spread of dengue: an optimal control simulation.- A. Torrado, A. Paula Barbosa-Póvoa, Chapter 13 – Towards an Optimized and Socio-Economic Blood Supply Chain Network.- Clara B. Vaz, ngela P. Ferreira, Chapter 14 – A DEA Approach to Evaluate the Performance of the Electric Mobility Deployment in European Countries.- D. B. Viana, B. B. Oliveira, Chapter 15 – The art of the deal: Machine learning based trade promotion evaluation.

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Book SynopsisThis book presents recent advances in the theory and application of the Best-Worst Method (BWM). It includes selected papers from the Third International Workshop on Best-Worst Method (BWM2022), held in Delft, the Netherlands, from 9 to 10 June 2022. The book provides valuable insights on why and how to use BWM in a diverse range of applications including health, energy, supply chain management, and engineering. Moreover, it highlights the use of BWM in different settings including individual decision-making vs group decision-making, and with complete information vs incomplete and uncertain information. Academics and practitioners whose work involves multi-criteria decision-making and decision analysis will particularly benefit from the papers gathered here.

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Book SynopsisThis volume comprises the thoroughly reviewed and revised papers of the First International Conference on New Trends in Applied Mathematics, ICNTAM 2022, which took place in Béni Mellal, Morocco, 19-21 May 2022.The papers deal with the following topics: Inverse Problems, Partial Differential Equations, Mathematical Control, Numerical Analysis and Computer Science. The main interest is in recent trends on Inverse Problems analysis and real applications in Computer Science. The latter is viewed as a dynamic branch on the interface of mathematics and related fields, that has been growing rapidly over the past several decades. However, its mathematical analysis and interpretation still not well-detailed and needs much more clarifications. The main contribution of this book is to give some sufficient mathematical content with expressive results and accurate applications. As a growing field, it is gaining a lot of attention both in media as well as in the industry world, which will attract the interest of readers from different scientist discipline. Table of ContentsA. Oulmelk, M. Srati and L. Afraites. Comparing numerical methods for inverse source problem in time-fractional diffusion equation.- S. Lyaqini. An improvement to the nonparametric regression models using the nonsmooth loss functions.- A. Nachaoui. Iterative methods for inverse problems subject to the convection-diffusion equation.- Y. Essadaoui, I. Hafidi. The dynamic behavior of an incompressible lubrication system.- M. Nachaoui, A. Nachaoui and M A hilal. A new approach for solving an inverse Cauchy problem based on BFGS method.- S. Lyaqini, M. Nachaoui. Heart failure prediction using supervised machine learning algorithms.- M. Srati, A. Oulmelk and L. Afraites. Optimization method for estimating the source term in elliptic equation.- A. Nachaoui. Cauchy's problem for the modified biharmonic equation: ill-posedness and Iterative regularizing methods.- A. Nachaoui and S. M. Rasheed. A mesh free wavelet method to solve the Cauchy problem for the Helmholtz equation.- A. Nachaoui, M. Nachaoui and T. Tadumadze. Meshless methods to noninvasively calculate neurocortical potentials from potentials measured at the scalp surface.- A. Nachaoui and F. Aboud. Solving geometric inverse problems with a polynomial based meshless method.- A. El-Hakoum, Z. Zaabouli and L. Afraites. On the analysis of a coupled denoising PDE.- M. Nachaoui, F. Jauberteau. A novel identification scheme of an inverse source problem based on Hilbert reproducing kernels.

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Book SynopsisThis volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.The 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.Table of ContentsA metaheuristic approach for solving Monitor Placement Problem.- A VNS-based heuristic for the minimum number of resources under a perfect schedule.- BVNS for Overlapping Community Detection.- A Simulation-Based Variable Neighborhood Search Approach for Optimizing Cross-Training Policies.- Multi-Objective Variable Neighborhood Search for improving software modularity.- An Effective VNS for Delivery Districting.- BVNS for the Minimum Sitting Arrangement problem in a cycle.- Assigning Multi-Skill Confgurations to Multiple Servers with a Reduced VNS.- Multi-Round Infuence Maximization: A Variable Neighborhood Search Approach.- A VNS based heuristic for a 2D Open Dimension Problem.- BVNS for the bi-objective multi row equal facility layout problem.

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Book SynopsisThis book constitutes the refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2023, held in Ekaterinburg, Russia, during July 2–8, 2023. The 28 full papers and 1 short paper included in this book were carefully reviewed and selected from 89 submissions. They were organized in topical sections as follows: Mathematical programming and applications; discrete and combinatorial optimization; stochastic optimization; scheduling; game theory; and optimal control and mathematical economics. The book also contains one invited talk in full paper length. Table of Contents​Invited papers.- General equilibrium models in production networks with substitution of inputs.- Mathematical programming and applications.- On decentralized nonsmooth optimization.- Byzantine-robust loopless stochastic variance-reduced gradient.- Semi-supervised k-means clustering via DC programming approach.- On the uniqueness of identification the thermal conductivity and heat capacit of substance.- On the uniqueness of identification the thermal conductivity and heat capacity of substance.- Discrete and combinatorial optimization.- Constant-factor approximation algorithms for some maximin multiclustering problems.- Aggregation tree construction using hierarchical structures.- Enumeration and unimodular equivalence of empty delta-modular simplices.- PTAS for p-means q-medoids r-given clustering problem.- Nested (2,3)-instances of the Cutting Stock Problem.- Stochastic optimization.- On the resource allocation problem to increase reliability of transport systems.- Distributionally robust optimization by probability criterion for estimating a bounded signal.- Scheduling.- Approximation algorithms for two-machine proportionate routing open shop on a tree.- MIP heuristics for a resource constrained project scheduling problem with workload stability constraints.- Hybrid evolutionary algorithm with optimized operators for total weighted tardiness problem.- Game theory.- Equilibrium arrivals to preemptive queueing system with fixed reward for completing request.- On optimal positional strategies in fractional optimal control problems.- On a single-type differential game of retention in a ring.- Harmonic numbers in Gambler’s Ruin Problem.- Exploitation and recovery periods in dynamic resource management problem.- Trade-off mechanism to sustain cooperation in pollution reduction.- Communication restriction-based characteristic function in differential games on networks.- Optimal control and mathematical economics.- Guaranteed expectation of the flock position with random distribution of items.- Method for solving a differential inclusion with a subdifferentiable support function of the right-hand side.- Approximate solution of small-time control synthesis problem based on linearization.- A Priori Estimates of the Objective Function in the Speed-in-Action Problem for a Linear Two-Dimensional Discrete-Time System.- An approach to solving input reconstruction problems in stochastic differential equations: dynamic algorithms and tuning their parameters.- Mathematical modeling of the household behavior on the labor market.- Visual positioning of a moving object using multi-objective control algorithm.

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Book SynopsisThis book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.Table of ContentsIntroduction.- The Traveling Salesman Problem (TSP).- The Nature of Heuristic Local Search.- he Attractor-Based Search System.- Solving Multi-objective TSP.- Solving Dynamic TSP.- Solving Probabilistic TSP.- Conclusion.

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Book SynopsisThis book constitutes the refereed proceedings of the 17th International Conference on Learning and Intelligent Optimization, LION-17, held in Nice, France, during June 4–8, 2023.The 40 full papers presented have been carefully reviewed and selected from 83 submissions. They focus on all aspects of unleashing the potential of integrating machine learning and optimization approaches, including automatic heuristic selection, intelligent restart strategies, predict-then-optimize, Bayesian optimization, and learning to optimize.Table of ContentsAnomaly Classification to Enable Self-Healing in Cyber Physical Systems using Process Mining.- Hyper-box Classification Model using Mathematical Programming.- A leak localization algorithm in water distribution networks using probabilistic leak representation and optimal transport distance.- Fast and Robust Constrained Optimization via Evolutionary and Quadratic Programming.- Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing.- A Bayesian optimization algorithm for constrained simulation optimization problems with heteroscedastic noise.- Hierarchical Machine Unlearning.- Explaining the Behavior of Reinforcement Learning Agents using Explaining the Behavior of Reinforcement Learning Agents using.- Deep Randomized Networks for Fast Learning.- Generative models via Optimal Transport and Gaussian Processes.- Real-world streaming process discovery from low-level event data.- Robust Neural Network Approach to System Identification in the High-Noise Regime.- GPU for Monte Carlo Search.- Learning the Bias Weights for Generalized Nested Rollout Policy Adaptation.- Heuristics selection with ML in CP Optimizer.- Model-based feature selection for neural networks: A mixed-integer programming approach.- An Error-Based Measure for Concept Drift Detection and Characterization.- Predict, Tune and Optimize for Data-Driven Shift Scheduling with Uncertain Demands.- On Learning When to Decompose Graphical Models.- Inverse Lighting with Differentiable Physically-Based Model.- Repositioning Fleet Vehicles: a Learning Pipeline.- Bayesian Decision Trees Inspired from Evolutionary Algorithms.- Towards Tackling MaxSAT by Combining Nested Monte Carlo with Local Search.- Relational Graph Attention-based Deep Reinforcement Learning: An Application to Flexible Job Shop Scheduling with Sequence-dependent Setup Times.- Experimental Digital Twin for Job Shops with Transportation Agents.- Learning to Prune Electric Vehicle Routing Problems.- A matheuristic approach for electric bus fleet scheduling.- Class GP: Gaussian Process Modeling for Heterogeneous Functions.- Surrogate Membership for Inferred Metrics in Fairness Evaluation.- The BeMi Stardust: a Structured Ensemble of Binarized Neural Network.- Discovering explicit scale-up criteria in crisis response with decision mining.- Job Shop Scheduling via Deep Reinforcement Learning: a Sequence to Sequence approach.- Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks.- Multi-Task Predict-then-Optimize.- Integrating Hyperparameter Search into Model-Free AutoML with Context-Free Grammars.- Improving subtour elimination constraint generation in Branch-and-Cut algorithms for the TSP with Machine Learning.- Learn, Compare, Search: One Sawmill’s Search for the Best Cutting Patterns Across And/or Trees.- Dynamic Police Patrol Scheduling with Multi-Agent Reinforcement Learning.- Analysis of Heuristics for Vector Scheduling and Vector Bin Packing.- Unleashing the potential of restart by detecting the search stagnation.

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Book SynopsisThis study guide is designed for students taking a Calculus II course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes applications of integration, sequences and series and their applications, polar coordinate systems, and complex numbers. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students’ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based coursesTable of ContentsChapter 1: Problems: Applications of integration.- Chapter 2: Solutions of Problems: Applications of integration.- Chapter 3: Problems: Sequences and series and their applications.- Chapter 4: Solutions of Problems: Sequences and series and their applications.- Chapter 5: Problems: Polar coordinate system.- Chapter 6: Solutions of Problems: Polar coordinate system.- Chapter 7: Problems: Complex numbers.- Chapter 8: Solutions of Problems: Complex numbers.

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Book SynopsisOn the morphism 1 ? 121, 2 ? 12221.- Polynomials and combinatorial identities.- Rainbow Greedy Matching Algorithms.- Predictive models of Non-Performing Loans: the case of Greece.- The Cost of Detection in Interaction Testing.- On the study of cycle chains representing non-reversible Markov chains associated with random walks with jumps in fixed environments.- Applying Distance Measures for Discrete Data.- Demand aggregation and mid-term energy planning problem on the business layer.- Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices.- A Code-based Watermarking Scheme for the Protection of Authenticity of Medical Images.- The minimum cost energy flow problem under demand uncertainty Effect on optimal solution, variability, worst and best case scenarios.- A mathematical study of the Braess's Paradox within a network comprising four nodes, five edges, and linear time functions.- On similiarities between two global optimization algorithms based on different (Bayesian and Lipschitzian) approaches.

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