Perturbation Analysis of Optimization Problems / Edition 1

by J.Frederic Bonnans, Alexander Shapiro

Overview

The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.

Product Details

ISBN-13:	9780387987057
Publisher:	Springer New York
Publication date:	05/11/2000
Series:	Springer Series in Operations Research and Financial Engineering
Edition description:	2000
Pages:	601
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

Basic notation.- Introduction.- Background material.- Optimality conditions.- Basic perturbation theory.- Second order analysis of the optimal value and optimal solutions.- Optimal Control.- References.