Edwin K. P. Chong, Stanislaw H. Zak

An Introduction to Optimization (eBook, PDF)

• Format: PDF

Produktbeschreibung

Praise for the Third Edition ". . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail." --MAA Reviews Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus. This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers: * A new chapter on integer programming * Expanded coverage of one-dimensional methods * Updated and expanded sections on linear matrix inequalities * Numerous new exercises at the end of each chapter * MATLAB exercises and drill problems to reinforce the discussed theory and algorithms * Numerous diagrams and figures that complement the written presentation of key concepts * MATLAB M-files for implementation of the discussed theory and algorithms (available via the book's website) Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 640
• Erscheinungstermin: 14. Juli 2014
• Englisch
• ISBN-13: 9781118523698
• Artikelnr.: 41209133

Autorenporträt

Edwin K. P. Chong, PHD, is Professor of Electrical and Computer Engineering as well as Professor of Mathematics at Colorado State University. He is a Fellow of the IEEE and Senior Editor of IEEE Transactions on Automatic Control. Stanislaw H. Zak, PHD, is Professor in the School of Electrical and Computer Engineering at Purdue University. He is former associate editor of Dynamics and Control and IEEE Transactions on Neural Networks

Inhaltsangabe

Preface xiii PART I MATHEMATICAL REVIEW 1 Methods of Proof and Some
Notation 3 1.1 Methods of Proof 3 1.2 Notation 5 Exercises 6 2 Vector
Spaces and Matrices 7 2.1 Vector and Matrix 7 2.2 Rank of a Matrix 13 2.3
Linear Equations 17 2.4 Inner Products and Norms 19 Exercises 22 3
Transformations 25 3.1 Linear Transformations 25 3.2 Eigenvalues and
Eigenvectors 26 3.3 Orthogonal Projections 29 3.4 Quadratic Forms 31 3.5
Matrix Norms 35 Exercises 40 4 Concepts from Geometry 45 4.1 Line Segments
45 4.2 Hyperplanes and Linear Varieties 46 4.3 Convex Sets 48 4.4
Neighborhoods 50 4.5 Polytopes and Polyhedra 52 Exercises 53 5 Elements of
Calculus 55 5.1 Sequences and Limits 55 5.2 Differentiability 62 5.3 The
Derivative Matrix 63 5.4 Differentiation Rules 67 5.5 Level Sets and
Gradients 68 5.6 Taylor Series 72 Exercises 77 PART II UNCONSTRAINED
OPTIMIZATION 6 Basics of Set-Constrained and Unconstrained Optimization 81
6.1 Introduction 81 6.2 Conditions for Local Minimizers 83 Exercises 93 7
One-Dimensional Search Methods 103 7.1 Introduction 103 7.2 Golden Section
Search 104 7.3 Fibonacci Method 108 7.4 Bisection Method 116 7.5 Newton's
Method 116 7.6 Secant Method 120 7.7 Bracketing 123 7.8 Line Search in
Multidimensional Optimization 124 Exercises 126 8 Gradient Methods 131 8.1
Introduction 131 8.2 The Method of Steepest Descent 133 8.3 Analysis of
Gradient Methods 141 Exercises 153 9 Newton's Method 161 9.1 Introduction
161 9.2 Analysis of Newton's Method 164 9.3 Levenberg-Marquardt
Modification 168 9.4 Newton's Method for Nonlinear Least Squares 168
Exercises 171 10 Conjugate Direction Methods 175 10.1 Introduction 175 10.2
The Conjugate Direction Algorithm 177 10.3 The Conjugate Gradient Algorithm
182 10.4 The Conjugate Gradient Algorithm for Nonquadratic Problems 186
Exercises 189 11 Quasi-Newton Methods 193 11.1 Introduction 193 11.2
Approximating the Inverse Hessian 194 11.3 The Rank One Correction Formula
197 11.4 The DFP Algorithm 202 11.5 The BFGS Algorithm 207 Exercises 211 12
Solving Linear Equations 217 12.1 Least-Squares Analysis 217 12.2 The
Recursive Least-Squares Algorithm 227 12.3 Solution to a Linear Equation
with Minimum Norm 231 12.4 Kaczmarz's Algorithm 232 12.5 Solving Linear
Equations in General 236 Exercises 244 13 Unconstrained Optimization and
Neural Networks 253 13.1 Introduction 253 13.2 Single-Neuron Training 256
13.3 The Backpropagation Algorithm 258 Exercises 270 14 Global Search
Algorithms 273 14.1 Introduction 273 14.2 The Nelder-Mead Simplex Algorithm
274 14.3 Simulated Annealing 278 14.4 Particle Swarm Optimization 282 14.5
Genetic Algorithms 285 Exercises 298 PART III LINEAR PROGRAMMING 15
Introduction to Linear Programming 305 15.1 Brief History of Linear
Programming 305 15.2 Simple Examples of Linear Programs 307 15.3
Two-Dimensional Linear Programs 314 15.4 Convex Polyhedra and Linear
Programming 316 15.5 Standard Form Linear Programs 318 15.6 Basic Solutions
324 15.7 Properties of Basic Solutions 327 15.8 Geometric View of Linear
Programs 330 Exercises 335 16 Simplex Method 339 16.1 Solving Linear
Equations Using Row Operations 339 16.2 The Canonical Augmented Matrix 346
16.3 Updating the Augmented Matrix 349 16.4 The Simplex Algorithm 350 16.5
Matrix Form of the Simplex Method 357 16.6 Two-Phase Simplex Method 361
16.7 Revised Simplex Method 364 Exercises 369 17 Duality 379 17.1 Dual
Linear Programs 379 17.2 Properties of Dual Problems 387 Exercises 394 18
Nonsimplex Methods 403 18.1 Introduction 403 18.2 Khachiyan's Method 405
18.3 Affine Scaling Method 408 18.4 Karmarkar's Method 413 Exercises 426 19
Integer Linear Programming 429 19.1 Introduction 429 19.2 Unimodular
Matrices 430 19.3 The Gomory Cutting-Plane Method 437 Exercises 447 PART IV
NONLINEAR CONSTRAINED OPTIMIZATION 20 Problems with Equality Constraints
453 20.1 Introduction 453 20.2 Problem Formulation 455 20.3 Tangent and
Normal Spaces 456 20.4 Lagrange Condition 463 20.5 Second-Order Conditions
472 20.6 Minimizing Quadratics Subject to Linear Constraints 476 Exercises
481 21 Problems with Inequality Constraints 487 21.1 Karush-Kuhn-Tucker
Condition 487 21.2 Second-Order Conditions 496 Exercises 501 22 Convex
Optimization Problems 509 22.1 Introduction 509 22.2 Convex Functions 512
22.3 Convex Optimization Problems 521 22.4 Semidefinite Programming 527
Exercises 540 23 Algorithms for Constrained Optimization 549 23.1
Introduction 549 23.2 Projections 549 23.3 Projected Gradient Methods with
Linear Constraints 553 23.4 Lagrangian Algorithms 557 23.5 Penalty Methods
564 Exercises 571 24 Multiobjective Optimization 577 24.1 Introduction 577
24.2 Pareto Solutions 578 24.3 Computing the Pareto Front 581 24.4 From
Multiobjective to Single-Objective Optimization 585 24.5 Uncertain Linear
Programming Problems 588 Exercises 596 References 599 Index 609