Multiobjective nonlinear second order symmetric duality with (K, F)-pseudoconvexity

Abstract

The purpose of this paper is to introduce a new class of generalized cone-pseudoconvex functions and strongly cone-pseudoconvex functions, called second order (K,F)-pseudoconvex functions and strongly second order (K,F)-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated over arbitrary generalized cone-pseudoconvex functions. For these second order symmetric dual programs, the weak, strong and converse duality theorems are established using the above generalization of cone-pseudoconvex functions. A self duality theorem is also given by assuming the functions involved to be skew-symmetric.