OPTIMALITY CONDITIONS FOR WEAK EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS

In this paper, we present a necessary as well as sufficient optimality condition for the weak efficient solution to the vector equilibrium problem with constraints VEPC in terms of contingent epiderivatives. First, we study some important properties of the contingent epiderivative of a single-valued mapping in Banach spaces. Second, we establish a Fritz John type necessary optimality condition for VEPC in terms of contingent epiderivatives. Under assumptions on quasiconvexity of scalar functions, a Fritz John type necessary optimality condition becomes a Fritz John type sufficient optimality condition.