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Well-Posed Optimization Problems

  • Book
  • © 1993

Overview

Authors:
  1. Asen L. Dontchev
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    You can also search for this author in PubMed   Google Scholar

  2. Tullio Zolezzi
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1543)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XII
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  2. Tykhonov well-posedness

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 1-37

  3. Hadamard and tykhonov well-posedness

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 38-80

  4. Generic well-posedness

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 81-115

  5. Well-posedness and variational, epi- and mosco convergences

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 116-175

  6. Well-posedness in optimal control

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 176-229

  7. Relaxation and value hadamard well-posedness in optimal control

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 230-247

  8. Singular perturbations in optimal control

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 248-282

  9. Well-posedness in the calculus of variations

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 283-334

  10. Hadamard well-posedness in mathematical programming

    • Asen L. Dontchev, Tullio Zolezzi
    Pages 335-380

  11. Back Matter

    Pages 381-421
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Keywords

About this book

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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