Viscosity-type Approximation Method for Efficient Solutions in Vector Optimization

Abstract

The paper is devoted to developing the viscosity-type approximation algorithm of finding efficient solutions to the vector optimization problem for a mapping between finite dimensional Hilbert spaces with respect to the partial order induced by a pointed closed convex cone. We prove that under some suitable conditions either the sequence generated by our method converges to an efficient solution or its cluster points belong to the set of all efficient solutions of this problem.