Vector Optimization: Theory, Applications, and Extensions

Product Description

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.
This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

Review

From the reviews:
“J. Jahn, well known by his papers and books on convex analysis and optimization a ] wrote this interesting book that gives a clear insight into theory and application of vector optimization. It is not only a revised version of the book from 1986 a ] but he also extended the contents considerably a ] .” (Alfred GApfert, Zentralblatt MATH, Vol. 1055, 2005)
“This volume is a revised and substantially enlarged version of the authora (TM)s book a ] . This excellent book will be very useful as an introduction to vector optimization and will also constitute a valuable reference for researchers. It will undoubtedly become a ] a classical reference in the field.” (Juan-Enrique Martinez-Legaz, Mathematical Reviews, 2005c)
“The book under review is dedicated to the theory of vector optimization in general spaces. a ] All at all, the book highlights very well recent developments in the field of active research a ] . The material is well presented, preliminaries are discussed in detail, and many illustrations help to understand the complicated facts. a ] may be warmly recommended to graduate students and researchers in optimization, numerical mathematics, operations research, engineering and other fields which apply optimization methods.” (C. Tammer, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 109 (4), 2007)

From the Back Cover

This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.
This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.