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.
Author(s): Johannes Jahn (auth.)
Edition: 2
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 481
Tags: Operations Research/Decision Theory; Optimization; Operations Research, Mathematical Programming
Front Matter....Pages i-xv
Front Matter....Pages 1-2
Linear Spaces....Pages 3-36
Maps on Linear Spaces....Pages 37-59
Some Fundamental Theorems....Pages 61-100
Front Matter....Pages 101-102
Optimality Notions....Pages 103-114
Scalarization....Pages 115-148
Existence Theorems....Pages 149-160
Generalized Lagrange Multiplier Rule....Pages 161-188
Duality....Pages 189-207
Front Matter....Pages 209-210
Vector Approximation....Pages 211-242
Cooperative n Player Differential Games....Pages 243-278
Front Matter....Pages 279-280
Theoretical Basics of Multiobjective Optimization....Pages 281-313
Numerical Methods....Pages 315-349
Multiobjective Design Problems....Pages 351-381
Front Matter....Pages 383-384
Basic Concepts and Results of Set Optimization....Pages 385-392
Contingent Epiderivatives....Pages 393-409
Subdifferential....Pages 411-421
Optimality Conditions....Pages 423-447
Back Matter....Pages 449-481
