Recent Developments in Well-Posed Variational Problems / Edition 1

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'Approximate solution' plays a central role in contemporary mathematics. This is due to the increasing complexity of the models and the related need to introduce simplifying assumptions and numerical approximations. Therefore, when dealing with any mathematical model, some of the basic questions to be asked are whether the solution is stable with respect to given perturbations, what the approximate solutions are, and if the set of the approximate solutions is close to the original solution set. Moreover, the connections between these aspects are of great interest also from a theoretical point of view. This volume contains articles describing and emphasizing the above-mentioned concepts of approximate solution, well-posedness and stability in optimization, calculus of variations, optimal control and mathematics of conflict, such as game theory and vector optimization. Particular attention is paid to the most recent developments of the theory. This book is of interest to researchers and graduate students working with variational problems, non-linear analysis, optimization and game theory.
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Editorial Reviews

For researchers and graduate students working with variational problems, non-linear analysis, optimization, and game theory, 11 articles address such basic questions about approximate solutions as whether the solution is stable with respect to given perturbations, what the approximate solutions are, and whether the set of the approximate solutions is close to the original solution set. In general they are concerned with applying familiar concepts to more complicated situations such as vector optimization, game theory, and variational inequalities. Among the specific topics are the minimax approach to the critical point theory, characterizations of Lipschitze stability in optimization, and hypertopologies. No index. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780792335764
  • Publisher: Springer Netherlands
  • Publication date: 6/30/1995
  • Series: Mathematics and Its Applications (closed) Series, #331
  • Edition description: 1995
  • Edition number: 1
  • Pages: 268
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.69 (d)

Table of Contents

A Survey on Old and Recent Results about the Gap Phenomenon in the Calculus of Variations 1
The Minimax Approach to the Critical Point Theory 29
Smooth Variational Principles and non Smooth Analysis in Banach Spaces 77
Characterizations of Lipschitz Stability in Optimization 95
Generic Well-posedness of Optimization Problems and the Banach-Mazur Game 117
Set-valued Interpolation, Differential Inclusions, and Sensitivity in Optimization 137
Well-posedness in Vector Optimization 171
Hypertopologies and Applications 193
Well-posedness for Nash equilibria and Related Topics 211
Various Aspects of Well-posedness of Optimization Problems 229
Well-posed Problems in the Calculus of Variations 257
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