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Springer Optimization and Its Applications #2: Optimization with Multivalued Mappings: Theory, Applications and Algorithmsby Stephan Dempe
Synopses & Reviews
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. Audience This book is intended for researchers, graduate students and practitioners in the fields of applied mathematics, operations research, and economics.
This book focuses on the tremendous development that has taken place recently in the field of of nondifferentiable nonconvex optimization. Coverage includes the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the co-derivative of Mordukhovich), the opening of new applications (the calibration of water supply systems), and the elaboration of new solution algorithms (e.g., smoothing methods).
Table of Contents
Preface.- PART I. BILEVEL PROGRAMMING.- Optimality conditions for bilevel programming problems (Stephan Dempe, Vyatcheslav V. Kalashnikov and Nataliya Kalashnykova).- Path-based formulations of a bilevel toll setting problem (Mohamed Didi-Biha, Patrice Marcotte and Gilles Savard).- Bilevel programming with convex lower level problems (Joydeep Dutta and Stephan Dempe).- Optimality criteria for bilevel programming problems using the radial subdifferential (D. Fanghänel).- On approximate mixed Nash equilibria and average marginal functions for two-stage three-players games (Lina Mallozzi and Jacqueline Morgan).- 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).- 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).- On the control of an evolutionary equilibrium in micromagnetics (Michal Kocvara, Martin Kruzík, Jirí V. Outrata).- Complementarity constraints as nonlinear equations: Theory and numerical experience (Sven Leyffer).- A semi-infinite approach to design centering (Oliver Stein).- PART III. SET-VALUED OPTIMIZATION.- Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities (Pham Ngoc Anh and Le Dung Muu).- Optimality conditions for a d.c. set-valued problem via the extremal principle (N. Gadhi).- First and second order optimality conditions in set optimization (V. Kalashnikov, B. Jadamba, A.A. Khan).
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