In this paper, we formulate a general dual problem for a class of nondifferentiable multiobjective programs involving the support function of a compact convex set and linear functions. Fritz John and Kuhn-Tucker optimality conditions are presented. In addition, we establish weak and strong duality theorems for weakly efficient solutions under suitable generalized (F, α, ρ, d) convexity assumptions. Some special cases of our duality results are given.

In this paper, we consider a class of nonsmooth multiobjective programming problems. Necessary and sufficient optimality conditions are obtained under higher order strongly convexity for Lipschitz functions. We formulate Mond-Weir type dual problem and establish weak and strong duality theorems for a strict minimizer of order m.

We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of properly efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given. Journal of Inequalities and ApplicationsDuality theorems for nondifferentiable programming problem with a square root term were obtained by Lal et al. 8 . In 1996, Mond and Schechter 9 studied duality and optimality for nondifferentiable multiobjective programming problems in which each component of the objective function contains the support functions of a compact convex sets. And Kuk et al. 10 defined the concept of V, ρ -invexity for vector-valued functions, which is a generalization of the concept of V -invexity concept.Recently, Yang et al. 11 introduced a class of nondifferentiable multiobjective programming problems involving the support functions of compact convex sets. They established only weak duality theorems for efficient solutions. Subsequently, Kim and Bae 12 formulated nondifferentiable multiobjective programs involving the support functions of a compact convex sets and linear functions.In this paper, we introduce generalized convex duality for nondifferentiable multiobjective program for efficient solutions. In Section 2 and Section 3, we formulate Mond-Weir type dual and Wolfe type dual problems and establish weak and strong duality under ρ-convexity assumptions. In addition, we obtain some special cases of our duality results in Section 4. Our duality results extend and improve well known duality results.

In this paper, we introduce nondifferentiable multiobjective fractional programming problems with cone constraints over arbitrary closed convex cones, where every component of the objective function contains a term involving the support function of a compact convex set. For this problem, Wolfe and Mond-Weir type duals are proposed. We establish weak and strong duality theorems for a weakly efficient solution under suitable (V, ρ)-invexity assumptions. As special cases of our duality relations, we give some known duality results.

In this paper, we consider a nonsmooth multiobjective programming problems including support functions with inequality and equality constraints. Necessary and sufficient optimality conditions are obtained by using higher-order strong convexity for Lipschitz functions. Mond-Weir type dual problem and duality theorems for a strict minimizer of order m are given.