Duality in vector optimization

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. 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