Second-Order Symmetric Duality for Multiple Objectives Nonlinear Programming Under Generalizations of Cone-Preinvexity Functions

Abstract

In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.