Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

Abstract

A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond−Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.

Keywords

• higher-order nondifferentiable programming
• symmetric duality
• self duality higher-order ℱ-convexity/higher-order ℱ-pseudoconvexity
• duality theorems