This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes. The monograph is closed with extensive considerations concerning conjugate duality for set-valued optimization problems.
Author(s): Radu Ioan Bot, Sorin-Mihai Grad, Gert Wanka (auth.)
Series: Vector Optimization
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 400
Tags: Operations Research, Mathematical Programming; Operations Research/Decision Theory; Discrete Mathematics in Computer Science
Front Matter....Pages 1-14
Introduction....Pages 1-7
Preliminaries on convex analysis and vector optimization....Pages 9-61
Conjugate duality in scalar optimization....Pages 63-121
Conjugate vector duality via scalarization....Pages 123-180
Conjugate duality for vector optimization problems with finite dimensional image spaces....Pages 181-247
Wolfe and Mond-Weir duality concepts....Pages 249-309
Duality for set-valued optimization problems based on vector conjugacy....Pages 311-383
Back Matter....Pages 1-15
