Overview
- Authors:
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Jiři Outrata
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Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
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Michal Kočvara
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Institute of Applied Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany
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Jochem Zowe
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Institute of Applied Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany
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Table of contents (12 chapters)
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Theory
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 3-11
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 13-42
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 43-68
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 69-84
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 85-102
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 103-123
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 125-147
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Applications
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Front Matter
Pages 149-149
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 151-153
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 155-179
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 181-202
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 203-215
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- Jiři Outrata, Michal Kočvara, Jochem Zowe
Pages 217-235
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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.
