Optimality Conditions for Multiobjective Programming with Generalized ([formula omitted], ρ, θ)-Convex Set Functions

Abstract

Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Lin (J. Math. Anal. Appl.132,1988, 558–571). In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfied; for instance (I,ρ,θ)-convexity is assumed for both objective and constraint set functions. Some duality models are also discussed. Wolfe-type and Mond–Weir-type duality theorems are proved.