Vector Optimization | Set-valued and Variational Analysis

Guang-Ya Chen (u. a.)

ISBN 10: 3540212892 / ISBN 13: 9783540212898

Published by Springer, 2005

About this Item

Vector Optimization | Set-valued and Variational Analysis | Guang-Ya Chen (u. a.) | Taschenbuch | x | Englisch | 2005 | Springer | EAN 9783540212898 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.

Seller Inventory # 102417195

Bibliographic Details

• Title: Vector Optimization | Set-valued and Variational Analysis
• Publisher: Springer
• Publication Date: 2005
• Language: English
• ISBN 10: 3540212892
• ISBN 13: 9783540212898
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 233W x 155H x 18D millimeters 233 millimeters width by 155 millimeters height by 18 millimeters depth
• Weight: 483 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu­ tion in 1896). Typical examples of vector optimization model include maxi­ mization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational in­ equality problems, rather than optimization problems, unless further assump­ tions are imposed. The vector variational inequality was introduced by Gi- nessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Nemeth (1980) has been an interesting topic in the last decade. Fan Ky's minimax theorems and minimax inequalities for real-valued func­ tions have played a key role in optimization theory, game theory and math­ ematical economics. An extension was proposed to vector payoffs was intro­ duced by Blackwell (1955).