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AuthorDontchev, Asen L. author
TitleWell-Posed Optimization Problems [electronic resource] / by Asen L. Dontchev, Tullio Zolezzi
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect tohttp://dx.doi.org/10.1007/BFb0084195
Descript XII, 424 p. online resource

SUMMARY

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


CONTENT

Tykhonov well-posedness -- Hadamard and tykhonov well-posedness -- Generic well-posedness -- Well-posedness and variational, epi- and mosco convergences -- Well-posedness in optimal control -- Relaxation and value hadamard well-posedness in optimal control -- Singular perturbations in optimal control -- Well-posedness in the calculus of variations -- Hadamard well-posedness in mathematical programming


Mathematics System theory Calculus of variations Economic theory Mathematics Systems Theory Control Calculus of Variations and Optimal Control; Optimization Economic Theory/Quantitative Economics/Mathematical Methods



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