Solving uncertain nonlinear complementarity problem by using a new penalty method

Abstract

In this paper, we develop a new class of uncertain nonlinear complemen-tarity problem (UNCP), that is, the uncertain nonlinear complementarity problem based on uncertainty theory in finite Euclidean spaces. It can be regarded as the generalization of classical nonlinear complementarity problem. In order to find the solution of the UNCP, we firstly convert it into an uncertain mathematical program with equilibrium constraints (UMPECs) by the expected value of uncertain variables. To go one step further, we construct an auxiliary function, which is used to convert the UMPECs into the reformulation of the problem. Then, we present a new penalty method for solving the UNCP. Finally, it is another core of the paper that the rigorous convergence of the penalty method has been proofed.