Some criteria for error bounds in set optimization

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of {\it all } Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions {\it corresponding to one} Pareto efficient/Henig proper … Read more

Optimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems

We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in … Read more

Optimality conditions for several type of efficient solutions of set-valued optimization problems

A simple unified framework is presented for the study of strong efficient solutions, weak efficient solutions, positive proper efficient solutions, Henig global proper efficient solutions, Henig proper efficient solutions, super efficient solutions, Benson proper efficient solutions, Hartley proper efficient solutions, Hurwicz proper efficient solutions and Borwein proper efficient solutions of set-valued optimization problem with/or without … Read more


In this paper we consider, for the first time, approximate Henig proper minimizers and approximate super minimizers of a set-valued map F with values in a partially ordered vector space and formulate two versions of the Ekeland variational principle for these points involving coderivatives in the senses of Ioffe, Clarke and Mordukhovich. As applications we … Read more