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Mathematics and Its Applications

Recent Developments in Well-Posed Variational Problems

Editors: Lucchetti, Roberto, Revalski, Julian (Eds.)

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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.

Table of contents (11 chapters)

Table of contents (11 chapters)
  • A Survey on Old and Recent Results about the Gap Phenomenon in the Calculus of Variations

    Pages 1-27

    Buttazzo, G. (et al.)

  • The Minimax Approach to the Critical Point Theory

    Pages 29-76

    Conti, M. (et al.)

  • Smooth Variational Principles and non Smooth Analysis in Banach Spaces

    Pages 77-94

    Deville, R.

  • Characterizations of Lipschitz Stability in Optimization

    Pages 95-115

    Dontchev, A. L.

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

    Pages 117-136

    Kenderov, P. S. (et al.)

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-94-015-8472-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-7923-3576-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-90-481-4578-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Recent Developments in Well-Posed Variational Problems
Editors
  • Roberto Lucchetti
  • Julian Revalski
Series Title
Mathematics and Its Applications
Series Volume
331
Copyright
1995
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8472-2
DOI
10.1007/978-94-015-8472-2
Hardcover ISBN
978-0-7923-3576-4
Softcover ISBN
978-90-481-4578-2
Edition Number
1
Number of Pages
VIII, 268
Topics