Variational Analysis and Generalized Differentiation II

Applications

  • Boris S. Mordukhovich

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 331)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Applications

    1. Front Matter
      Pages 1-1
    2. Boris S. Mordukhovich
      Pages 3-158
    3. Boris S. Mordukhovich
      Pages 159-334
    4. Boris S. Mordukhovich
      Pages 335-459
    5. Boris S. Mordukhovich
      Pages 461-505
  3. Back Matter
    Pages 507-610

About this book

Introduction

Variational analysis has been recognized as a fruitful area in mathematics that on the one hand deals with the study of optimization and equilibrium problems and on the other hand applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational natur. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the hear of variational analysis and its applications.

This monographs contains a comprehensive and and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite dimensional spaces and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The book is published in two volumes, the first of which is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries.

This book will be of interest to researchers and graduate students in mathematical sciences. It may also be useful to a broad range of researchers, practitioners, and graduate students involved in the study and applications of variational methods in economics, engineering, control systems, operations research, statistics, mechanics, and other applied sciences.

Keywords

differential inclusions economics equilibria evolution systems multi-objective optimization optimal control optimization partial differential equations

Authors and affiliations

  • Boris S. Mordukhovich
    • 1
  1. 1.College of Science, Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-31246-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-25438-6
  • Online ISBN 978-3-540-31246-8
  • Series Print ISSN 0072-7830
  • About this book