Duality in Vector Optimization - Bot, Radu Ioan.; Grad, Sorin-Mihai.; Wanka, Gert.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2009)
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.
Preliminaries on convex analysis and vector optimization -- Conjugate duality in scalar optimization -- Conjugate vector duality via scalarization -- Conjugate duality for vector optimization problems with finite dimensional image spaces -- Wolfe and Mond-Weir duality concepts -- Duality for set-valued optimization problems based on vector conjugacy.
Keywords: Mathematics; Operations research; Decision making; Computer science -- Mathematics; Mathematical models; Management science; Mathematics; Mathematical Modeling and Industrial Mathematics; Operations Research, Management Science; Operation Research/Decision Theory; Discrete Mathematics in Computer Science; Electronic books