Numerical Optimization

Theoretical and Practical Aspects

Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizabal

432 pages, parution le 18/02/2003

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Résumé

Numerical Optimization has numerous applications in engineering sciences, operations research, economics, finance, etc. Starting with illustrations of this ubiquitous character, this book is essentially devoted to numerical algorithms for optimization, which are exposed in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems.

The theoretical bases of the subject, such as optimality conditions, Lagrange multipliers or duality, although recalled, are assumed known. Most of the algorithms described in the book are explained in a detailed manner, allowing straightforward implementation.

This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions.

Contents

Preliminaries

General Introduction

Part I Unconstrained Problems

Line-Searches
Newtonian Methods
Conjugate Gradient
Special Methods

Part II Nonsmooth Optimization

Some Theory of Nonsmooth Optimization
Some Methods in Nonsmooth Optimization
Bundle Methods. The Quest of Descent
Decomposition and Duality

Part III Newton's Methods in Constrained Optimization

Background
Local Methods for Problems with Equality Constraints
Local Methods for Problems with Equality and Inequality Constraints
Exact Penalization
Globalization by Line-Search
Quasi-Newton Versions

Part IV Interior-Point Algorithms for Linear and Quadratic Optimization

Linearly Constrained Optimization and Simplex Algorithm
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

L'auteur - Frédéric Bonnans

Frédéric Bonnans est directeur de recherche à l'INRIA et professeur chargé de cours à l'École Polytechnique.

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L'auteur - J. Charles Gilbert

INRIA Rocquencourt, Le Chesnay, France

L'auteur - Claude Lemaréchal

INRIA Rhône-Alpes, Montbonnot, France

L'auteur - Claudia A. Sagastizabal

IMPA, Rio de Janeiro, Brazil

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizabal
Parution	18/02/2003
Nb. de pages	432
Format	15,5 x 23,5
Couverture	Broché
Poids	650g
Intérieur	Noir et Blanc
EAN13	9783540001911