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Recent Developments in Well-Posed Variational Problems

  • Book
  • © 1995

Overview

Editors:
  1. Roberto Lucchetti

    1. Department of Mathematics, University of Milan, Milan, Italy

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  2. Julian Revalski

    1. Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 331)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
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  2. A Survey on Old and Recent Results about the Gap Phenomenon in the Calculus of Variations

    • G. Buttazzo, M. Belloni
    Pages 1-27

  3. The Minimax Approach to the Critical Point Theory

    • M. Conti, R. Lucchetti
    Pages 29-76

  4. Smooth Variational Principles and non Smooth Analysis in Banach Spaces

    • R. Deville
    Pages 77-94

  5. Characterizations of Lipschitz Stability in Optimization

    • A. L. Dontchev
    Pages 95-115

  6. Generic Well-Posedness of Optimization Problems and the Banach-Mazur Game

    • P. S. Kenderov, J. P. Revalski
    Pages 117-136

  7. Set-Valued Interpolation, Differential Inclusions, and Sensitivity in Optimization

    • F. Lempio
    Pages 137-169

  8. Well-posedness in Vector Optimization

    • P. Loridan
    Pages 171-192

  9. Hypertopologies and Applications

    • R. Lucchetti
    Pages 193-209

  10. Well-Posedness for Nash Equilibria and Related Topics

    • F. Patrone
    Pages 211-227

  11. Various Aspects of Well-Posedness of Optimization Problems

    • J. P. Revalski
    Pages 229-256

  12. Well-Posed Problems in the Calculus of Variations

    • T. Zolezzi
    Pages 257-266

  13. Back Matter

    Pages 267-268
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Keywords

About this book

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well­ posed problem.

Editors and Affiliations

  • Department of Mathematics, University of Milan, Milan, Italy

    Roberto Lucchetti

  • Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Julian Revalski

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