Complex analysis methods related an optimization problem with complex variables

Abstract

In this paper, we consider a nondifferentiable minimax fractional programming problem treated with complex variables. Duality problem in optimization theory plays an important role. The goal of this paper is to formulate the Wolfe type dual and Mond-Weir type dual problems. We aim to establish the duality problems, and prove that the duality theorems have no duality gap to the primal problem under some assumptions. The processes involves to show three theorems: the weak, strong and strictly converse duality theorem. 2000 Mathematics Subject Classifications: 26A51, 32C15, 90C32, 90C46