Optimization with Multivalued Mappings: Theory, Applications and Algorithms

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Stephan Dempe, Porfiria Raskolnikova
Springer Science & Business Media, Sep 19, 2006 - Mathematics - 276 pages
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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.

 

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Contents

Optimality conditions for bilevel programming problems
3
Pathbased formulations of a bilevel toll setting problem
29
Bilevel programming with convex lower level problems
51
Optimality criteria for bilevel programming problems using the radial subdifferential
73
On approximate mixed Nash equilibria and average marginal functions for twostage threeplayers games
96
A direct proof for Mstationarity under MPECGCQ for mathematical programs with equilibrium constraints
109
On the use of bilevel programming for solving a structural optimization problem with discrete variables
123
On the control of an evolutionary equilibrium in micromagnetics
143
Theory and numerical experience
169
A semiinfinite approach to design centering
209
Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities
231
Optimality conditions for a dc setvalued problem via the extremal principle
250
First and second order optimality conditions in set optimization
265
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