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  • © 1998

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Theory, Applications and Numerical Results

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxi
  2. Theory

    1. Front Matter

      Pages 1-1
    2. Introduction

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 3-11
    3. Auxiliary Results

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 13-42
    4. Algorithms of Nonsmooth Optimization

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 43-68
    5. Generalized Equations

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 69-84
    6. Stability of Solutions to Perturbed Generalized Equations

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 85-102
    7. Derivatives of Solutions to Perturbed Generalized Equations

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 103-123
    8. Optimality Conditions and a Solution Method

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 125-147
  3. Applications

    1. Front Matter

      Pages 149-149
    2. Introduction

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 151-153
    3. Membrane with Obstacle

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 155-179
    4. Elasticity Problems with Internal Obstacles

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 181-202
    5. Contact Problem with Coulomb Friction

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 203-215
    6. Economic Applications

      • Jiři Outrata, Michal Kočvara, Jochem Zowe
      Pages 217-235
  4. Back Matter

    Pages 237-273

About this book

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.

Authors and Affiliations

  • Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic

    Jiři Outrata

  • Institute of Applied Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany

    Michal Kočvara, Jochem Zowe

Bibliographic Information

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access