Existence of Solutions and Variational Principles for Generalized Vector Systems.

By means of generalized KKM theory, we prove a result on the existence of solutions and we establish general variational principles, that is, vector optimization formulations of set-valued maps for vector generalized systems. A perturbation function is involved in general variational principles. We extend the theory of gap functions for vector variational inequalities to vector generalized systems and we prove that the solution sets of the related vector optimization problems of set-valued maps contain the solution sets of vector generalized systems. A further vector optimization problem is defined in such a way that its solution set coincides with the solution set of a weak vector generalized system. [ABSTRACT FROM AUTHOR]