Recent Developments in Well-Posed Variational Problems / Edition 1

Recent Developments in Well-Posed Variational Problems / Edition 1

by Roberto Lucchetti
     
 

ISBN-10: 0792335767

ISBN-13: 9780792335764

Pub. Date: 06/30/1995

Publisher: Springer Netherlands

'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…  See more details below

Overview

'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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Product Details

ISBN-13:
9780792335764
Publisher:
Springer Netherlands
Publication date:
06/30/1995
Series:
Mathematics and Its Applications (closed) Series, #331
Edition description:
1995
Pages:
268
Product dimensions:
6.10(w) x 9.45(h) x 0.03(d)

Table of Contents

Introduction
A Survey on Old and Recent Results about the Gap Phenomenon in the Calculus of Variations1
The Minimax Approach to the Critical Point Theory29
Smooth Variational Principles and non Smooth Analysis in Banach Spaces77
Characterizations of Lipschitz Stability in Optimization95
Generic Well-posedness of Optimization Problems and the Banach-Mazur Game117
Set-valued Interpolation, Differential Inclusions, and Sensitivity in Optimization137
Well-posedness in Vector Optimization171
Hypertopologies and Applications193
Well-posedness for Nash equilibria and Related Topics211
Various Aspects of Well-posedness of Optimization Problems229
Well-posed Problems in the Calculus of Variations257

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