New second-order necessary optimality conditions for constrained vector optimization problems

Abstract

This paper is devoted to second-order optimality conditions of constrained vector optimization problems with continuously Fréchet differentiable data. Different from conventional approaches, we employ a new one, image space analysis, to establish suitable regularity conditions and then present new second-order necessary optimality conditions that depend on one single KKT multiplier for all critical directions. Moreover, we propose one more regularity condition for the multiobjective case and compare it with the previous one. Besides, we compare the main regularity conditions with the existing ones in the literature for the scalar case.