Advertisement

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Theory, Applications and Numerical Results

  • Jiři Outrata
  • Michal Kočvara
  • Jochem Zowe

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 28)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 3-11
    3. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 13-42
    4. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 43-68
    5. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 69-84
    6. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 85-102
    7. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 103-123
    8. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 125-147
  3. Applications

    1. Front Matter
      Pages 149-149
    2. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 151-153
    3. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 155-179
    4. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 181-202
    5. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 203-215
    6. Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 217-235
  4. Back Matter
    Pages 237-273

About this book

Introduction

In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.

Keywords

Newton's method Optimality Conditions algorithm algorithms calculus continuum mechanics mechanics modeling operations research optimization

Authors and affiliations

  • Jiři Outrata
    • 1
  • Michal Kočvara
    • 2
  • Jochem Zowe
    • 2
  1. 1.Institute of Information Theory and AutomationCzech Academy of SciencesPragueCzech Republic
  2. 2.Institute of Applied MathematicsUniversity of Erlangen-NurembergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2825-5
  • Copyright Information Springer-Verlag US 1998
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4804-5
  • Online ISBN 978-1-4757-2825-5
  • Series Print ISSN 1571-568X
  • Buy this book on publisher's site
Industry Sectors
Electronics