Numerical Optimization: Theoretical and Practical Aspects

by Joseph-Frïdïric Bonnans, Jean Charles Gilbert, Claude Lemarechal, Claudia A. Sagastizïbal

Overview

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.

Product Details

ISBN-13:	9783540354451
Publisher:	Springer Berlin Heidelberg
Publication date:	11/13/2006
Series:	Universitext
Edition description:	2nd ed. 2006
Pages:	494
Product dimensions:	6.10(w) x 9.20(h) x 1.10(d)

About the Author

The four authors are leading international specialists in various branches of nonlinear optimization (one of them received the Dantzig Prize). They are working - or have worked - at INRIA, the French National Institute for Research in Computer Science and Control, and they also teach in various universities and "Grandes Écoles". All of them continually collaborate with industry on problems dealing with optimization, in fields such as energy management, geoscience, life sciences, etc.

Table of Contents

Unconstrained Problems.- General Introduction.- Basic Methods.- Line-Searches.- Newtonian Methods.- Conjugate Gradient.- Special Methods.- A Case Study: Seismic Reection Tomography.- Nonsmooth Optimization.- to Nonsmooth Optimization.- Some Methods in Nonsmooth Optimization.- Bundle Methods. The Quest for Descent.- Applications of Nonsmooth Optimization.- Computational Exercises.- Newton's Methods in Constrained Optimization.- Background.- Local Methods for Problems with Equality Constraints.- Local Methods for Problems with Equality and InequalityConstraints.- Exact Penalization.- Globalization by Line-Search.- Quasi-Newton Versions.- Interior-Point Algorithms for Linear and QuadraticOptimization.- Linearly Constrained Optimization and SimplexAlgorithm.- Linear Monotone Complementarity and Associated Vector Fields.- Predictor-Corrector Algorithms.- Non-Feasible Algorithms.- Self-Duality.- One-Step Methods.- Complexity of Linear Optimization Problems with Integer Data.- Karmarkar's Algorithm.

Editorial Reviews

From the reviews of the second edition:

"This volume is a collection of four coordinated monographs on topics in numerical optimization. … the four sections of the book fit together to provide a broad survey of methods for numerical optimization at an advanced level. … this book should be of interest to advanced graduate students and researchers working in numerical optimization." (Brian Borchers, MathDL, March, 2007)

"More realistic application problems are introduced with the emphasis on outlining a typical modeling process in more detail. … the presentation of theoretical results on nonsmooth optimization is reorganized and contains now a new subsection with convergence results. The book provides an excellent basis for studying optimization theory and algorithms, especially for nonsmooth optimization. Additional case studies, availability of computer codes, and exercises improve the understanding of numerical algorithms and the practical problem solving process. In summary, the second edition significantly improves the first one." (Klaus Schittkowski, Zentralblatt MATH, Vol. 1108 (10), 2007)

From the Publisher