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OPTIMALITY CONDITIONS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS WITH GENERAL INEQUALITY CONSTRAINTS

. In this paper, we study a nonsmooth multiobjective optimization problem involving an equality constraint, a general inequality constraint and a set constraint, in which the general inequality constraint is of the form g ( x ) ∈ D with D a closed set. If D is a cone, this problem is reduced to a multiobjective optimiztion problem with cone-constraints. Under suitable conditions, necessary optimality conditions for weakly efﬁcient solutions in terms of the Clarke subdifferentials are established. With some assumptions of generalized convexity, sufﬁcient optimality conditions are derived. Weak and strong duality theorems of the Mond-Weir and Wolfe types are also given.