Optimization With Multivalued Mappings

by Dempe, Stephan; Kalashnikov, Vyacheslav

• ISBN13: 9780387342207
• ISBN10: 0387342206
• Format: Hardcover
• Copyright: 2006-08-04
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	ix
Part I Bilevel Programming
Optimality conditions for bilevel programming problems
Stephan Dempe, Vyatcheslav V. Kalashnikov and Nataliya Kalashnykova	3	(26)
Path-based formulations of a bilevel toll setting problem
Mohamed Didi-Biha, Patrice Marcotte and Gilles Savard	29	(22)
Bilevel programming with convex lower level problems
Joydeep Dutta and Stephan Dempe	51	(22)
Optimality criteria for bilevel programming problems using the radial subdifferential
D. Fanghänel	73	(24)
On approximate mixed Nash equilibria and average marginal functions for two-stage three-players games
Lima Mallozzi and Jacqueline Morgan	97	(14)
Part II Mathematical Programs with Equilibrium Constraints
A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints
Michael L. Flegel and Christian Kanzow	111	(12)
On the use of bilevel programming for solving a structural optimization problem with discrete variables
Joaquim J. Júdice, Ana M. Faustino, Isabel M. Ribeiro and A. Serra Neves	123	(20)
On the control of an evolutionary equilibrium in micromagnetics
Michal Kocvara, Marlin Kružik, Jiri V. Outrata	143	(26)
Complementarity constraints as nonlinear equations: Theory and numerical experience
Sven Leyffer	169	(40)
A semi-infinite approach to design centering
Oliver Stein	209	(22)
Part III Set-Valued Optimization
Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities
Pham Ngoc Anh and Le Dung Muu	231	(20)
Optimality conditions for a d.c. set-valued problem via the extremal principle
N. Gadhi	251	(14)
First and second order optimality conditions in set optimization
V. Kalashnil;ov, B. Jadamba, A.A. Khan	265