Optimality Conditions and Duality for a Class of Nondifferentiable Multiobjective Programming Problems

Abstract

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.

Optimality and Duality Theorems in Nonsmooth Multiobjective Optimization

“…In 2008, Kim and Bae [13] formulated nondifferentiable multiobjective programs involving the support functions of a compact convex sets. Also, Bae et al [14] established duality theorems for nondifferentiable multiobjective programming problems under generalized convexity assumptions.…”

Optimality conditions and duality for nondifferentiable multiobjective programming

“…The optimality conditions for the weak efficient solution, efficient solution and properly efficient solution and the duality results in multiobjective programming problems have attracted many researchers in recent years. For example, we can see in [3][4][5][6][7][8][9][10]. Recently, many researchers have been interested in other types of solution concepts, one of them is higher order strict minimizer.…”

Efficiency in Multiobjective Programming with Generalized Invexity

“…In particular, the sufficient optimality conditions and duality results for the nondifferentiable multiobjective programming problems were obtained by Kim [9][10] and Jayswal [11] under the generalized convex functions. Also, we can see the references in Ref.…”