GENERALIZED PROXIMAL METHOD FOR EFFICIENT SOLUTIONS IN VECTOR OPTIMIZATION

This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed convex cone. In contrast to most published literature on this subject, our algorithm does not depend on the nonemptiness of ordering cone of the space under consideration and deals with finding efficient solutions of the vector optimization problem in question. We prove that under some suitable conditions the sequence generated by our method weakly converges to an efficient solution of this problem.