OPTIMALITY CONDITIONS FOR MULTIOBJECTIVE PROGRAMMING WITH GENERALIZED(I,RHO,THETA)-CONVEX SET-FUNCTIONS

Necessary conditions for Pareto optimality in multiobjective programmi ng 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 f easible solution of such a problem will be Pareto optimal provided tha t a weaker convexity requirement is satisfied; for instance (F, rho th eta)-convexity is assumed for both objective and constraint set functi ons. Some duality models are also discussed. Wolfe-type and Mond-Weir- type duality theorems are proved. (C) 1997 Academic Press.