Strict directional solutions in vectorial problems: necessary optimality conditions (Q2070365)

In this paper the authors investigate the usage of directional strict efficiency in vector optimization problems with multifunctions as objectives. Different types of necessary optimality conditions derived with the help of generalized differentation tools such as Mordukhovich's subdifferentials, Clarke's penalization under suitable assumptions are presented. There are also shown that the directional strict efficiency works pretty well for vectorial equilibrium problems. The new concept of directional equilibrium points called as eigenvalue-vector equilibria coincide with directional strict minima under strong quasiconvexity of set-valued functions. The concept of directional strict efficiency covers the strict minimality for the case of scalar functions and the strict minimality in all directions relates to the global minimality.