Well-Posed Optimization Problems

Asen L. Dontchev, Tullio Zolezzi (auth.)0387567372, 9780387567372, 3540567372

This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov well-posedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs are provided. The expected knowledge of the reader does not extend beyond textbook (real and functional) analysis, some topology and differential equations and basic optimization. References are provided for more advanced topics. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.

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Table of contents :
Tykhonov well-posedness….Pages 1-37
Hadamard and tykhonov well-posedness….Pages 38-80
Generic well-posedness….Pages 81-115
Well-posedness and variational, epi- and mosco convergences….Pages 116-175
Well-posedness in optimal control….Pages 176-229
Relaxation and value hadamard well-posedness in optimal control….Pages 230-247
Singular perturbations in optimal control….Pages 248-282
Well-posedness in the calculus of variations….Pages 283-334
Hadamard well-posedness in mathematical programming….Pages 335-380