Numerical Optimization: Theoretical and Practical Aspects (Universitext)

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded. Title......Page 1 Preface......Page 3 Table of Contents......Page 5 1 General Introduction......Page 14 2 Basic Methods......Page 34 3 Line-Searches......Page 45 4 Newtonian Methods......Page 59 5 Conjugate Gradient......Page 75 6 Special Methods......Page 85 7 A Case Study: Seismic Reection Tomography......Page 105 8 Introduction to Nonsmooth Optimization......Page 115 9 Some Methods in Nonsmooth Optimization......Page 125 10 Bundle Methods. The Quest for Descent......Page 143 11 Applications of Nonsmooth Optimization......Page 166 12 Computational Exercises......Page 188 13 Background......Page 201 14 Local Methods for Problems with Equality Constraints......Page 219 15 Local Methods for Problems with Equality and Inequality Constraints......Page 258 16 Exact Penalization......Page 274 17 Globalization by Line-Search......Page 291 18 Quasi-Newton Versions......Page 325 19 Linearly Constrained Optimizationand Simplex Algorithm......Page 353 20 Linear Monotone Complementarityand Associated Vector Fields......Page 370 21 Predictor-Corrector Algorithms......Page 394 22 Non-Feasible Algorithms......Page 409 23 Self-Duality......Page 422 24 One-Step Methods......Page 432 25 Complexity of Linear OptimizationProblems with Integer Data......Page 448 26 Karmarkar's Algorithm......Page 454 References......Page 461 Index......Page 481

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions.

This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition of Numerical Optimization contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation. Features illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. This book covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems