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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.

Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones