Optimization with Multivalued Mappings

Theory, Applications, and Algorithms

  • Stephan Dempe
  • Vyacheslav Kalashnikov

Part of the Springer Optimization and Its Applications book series (SOIA, volume 2)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Bilevel Programming

    1. Front Matter
      Pages 1-1
    2. Stephan Dempe, Vyatcheslav V. Kalashnikov, Nataliya Kalashnykova
      Pages 3-28
    3. Mohamed Didi-Biha, Patrice Marcotte, Gilles Savard
      Pages 29-50
    4. Joydeep Dutta, Stephan Dempe
      Pages 51-71
  3. Mathematical Programs with Equilibrium Constraints

    1. Front Matter
      Pages 109-109
    2. Joaquim J. Júdice, Ana M. Faustino, Isabel M. Ribeiro, A. Serra Neves
      Pages 123-142
    3. Michal Kočvara, Martin Kružík, Jiří V. Outrata
      Pages 143-168
  4. Set-Valued Optimization

About this book

Introduction

In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods).

The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems.

 

Audience

This book is intended for researchers, graduate students and practitioners in the fields of applied mathematics, operations research, and economics.

Keywords

Bilevel programming Nonconvex programming Nondifferentiable programming Optimality conditions SOIA Solution algorithms algorithms optimization

Editors and affiliations

  • Stephan Dempe
    • 1
  • Vyacheslav Kalashnikov
    • 2
  1. 1.TU Bergakademie FreibergGermany
  2. 2.ITESMMonterreyMexico

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-34221-4
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-34220-7
  • Online ISBN 978-0-387-34221-4
  • Series Print ISSN 1931-6828
  • About this book