Generalizations of second-order pseudo-convexity functions for vector optimization problems under second-order symmetric duality

Abstract

Abstract In this work, we present new classes of second-order pseudo-convex functions and strong second-order pseudo-convex functions that generalize the second-order pseudo-convex functions. A pair of Mond-Weir type second-order symmetric duality multiple objective nonlinear programming problems formulate arbitrarily over these generalized second-order pseudo-convex functions. Furthermore, the weak, strong, and converse duality theorems are established and proven under these generalized second-order pseudo-convex functions. Finally, we present two nontrivial numerical examples to verify the results of the weak duality theorem and the strong duality theorem. MS Classifications: 90-XX 90CXX 90C30 90C46 65K05 49M37 49N15