Symmetric and self duality in vector optimization problem

In this paper, we present the first-order symmetric and self duality programs in multiobjective nonlinear programming problems. For these first-order symmetric and dual programs, we introduce the weak, strong, and converse duality theorems under convexity and concavity conditions, where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in [D.S. Kim, Y.B. Yun, H. Kuk, Second-order symmetric and self duality in multiobjective programming. Appl. Math. Lett. 10(2) (1997) 17-22]. Also, we prove the self duality theorem for these first-order self dual programs and illustrate its example.