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.
Highlights
The study of higher-order duality has computational advantages over the first-order duality when approximations are used, as it provides tighter bound for the value of the objective function
Mangasarian [1] formulated a class of higher-order duality in nonlinear problems
We show that the function φ( x ) is a higher-order F - pseudoconvex at u = 1 and for all x ≥ 1
Summary
The study of higher-order duality has computational advantages over the first-order duality when approximations are used, as it provides tighter bound for the value of the objective function. A higher-order Mond–Weir-type nondifferentiable multiobjective dual problem is formulated and established duality relations involving higher-order ( F, α, ρ, d) type-I fuctions by Ahmad et al [6]. Under K-preinvexity and K-pseudoinvexity assumptions, Ahmad and Husain [8] formulated multiobjective mixed type symmetric dual programs over cones and proved duality results. Xu [10] proved duality theorems for two mixed type duals of a multiobjective programming problem. Presented mixed type symmetric duality for nondifferentiable nonlinear programming problems. Symmetry 2020, 12, 274 higher-order nondifferentiable mixed symmetric dual model and duality results are studied under higher-order invexity/generalized invexity. A new mixed type nondifferentiable higher-order symmetric dual programs over cones are formulated. 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
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