Multiobjective optimization method for solving nonlinear complementarity problem

In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization. In this paper, we propose a new method for the NCP under the condition that the solution exists. We formulate the NCP into a multiobjective optimization problem (MOP), and define zero-efficient solution of MOP. Then we indicate that zero-efficient solution of the MOP is also the solution to the NCP. Finally we use minimax method for the MOP. Numerical results indicate that the proposed method is promising.