Vector Optimization
Theory, Applications, and Extensions
1st Edition
Published on 30. November 2010
Book
Paperback/Softback
XIII, 465 pages
978-3-642-05828-8 (ISBN)
Description
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.
Reviews / Votes
From the reviews:"J. Jahn, well known by his papers and books on convex analysis and optimization . 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 . but he also extended the contents considerably .." (Alfred Göpfert, Zentralblatt MATH, Vol. 1055, 2005)"This volume is a revised and substantially enlarged version of the author's book .. 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 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. . All at all, the book highlights very well recent developments in the field of active research .. The material is well presented, preliminaries are discussed in detail, and many illustrations help to understand the complicated facts. . 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)More details
Edition
1., st Edition. Softcover version of original hardcover edition 2004
Language
English
Place of publication
Berlin
Germany
Target group
Professional and scholarly
Research
Edition type
New edition
Illustrations
62 s/w Abbildungen, 14 s/w Tabellen
62 black & white illustrations, 14 black & white tables
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
718 gr
ISBN-13
978-3-642-05828-8 (9783642058288)
Schweitzer Classification
Other editions
Additional editions
E-Book
06/2013
1st Edition
Springer
€85.59
Available for download
Book
01/2004
Springer
€85.59
Article exhausted; check for reprint
Content
Convex Analysis: Linear Spaces.- Maps on Linear Spaces.- Some Fundamental Theorems.- Theory of Vector Optimization: Optimality Notions.- Scalarization.- Existence Theorems.- Generalized Lagrange Multiplier Rule.- Duality.- Mathematical Applications: Vector Approximation.- Cooperative n Player Differential Games.- Engineering Applications: Theoretical Basics of Multiobjective Optimization.- Numerical Methods.- Multiobjective Design Problems.- Extensions to Set Optimization: Basic Concepts and Results of Set Optimization.- Contingent Epiderivatives.- Subdifferential.- Optimality Conditions.