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.

Résumé
Thecontinuousandincreasinginterestconcerningvectoroptimizationperc- tible in the research community, where contributions dealing with the theory of duality abound lately, constitutes the main motivation that led to writing this book. Decisive was also the research experience of the authors in this ?eld, materialized in a number of works published within the last decade. The need for a book on duality in vector optimization comes from the fact that despite the large amount of papers in journals and proceedings volumes, no book mainly concentrated on this topic was available so far in the scienti?c landscape. There is a considerable presence of books, not all recent releases, on vector optimization in the literature. We mention here the ones due to Chen,HuangandYang(cf. [49]),EhrgottandGandibleux(cf. [65]),Eichfelder (cf. [66]), Goh and Yang (cf. [77]), G¨ opfert and Nehse (cf. [80]), G¨ opfert, - ahi, Tammer and Z? alinescu (cf. [81]), Jahn (cf. [104]), Kaliszewski (cf. [108]), Luc (cf. [125]), Miettinen (cf. [130]), Mishra, Wang and Lai (cf. [131,132]) and Sawaragi, Nakayama and Tanino (cf. [163]), where vector duality is at most tangentially treated. We hope that from our e?orts will bene?t not only researchers interested in vector optimization, but also graduate and und- graduate students. The framework we consider is taken as general as possible, namely we work in (locally convex) topological vector spaces, going to the usual ?nite - mensional setting when this brings additional insights or relevant connections to the existing literature.

Contenu
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.