A Wide-Neighborhood Algorithm for Monotone Nonlinear Complementarity Problem

In this paper we propose a new potential reduction interior-point method for monotone nonlinear complementarity problem, which based on the wide-neighborhood N_infin ^-(beta). Our method is ageneralization of Mizuno, Todd and Ye´s result. Although the search direction of it is the same as that of the path-following algorithm, the step size is determined as the minimum point of the potential function in the neighborhood. Therefore, the duality gap is reduced by a fixed positive constant at each step. Finally, the polynomial complexity O(nt) is attained when the problem satisfies a scaled Lipschitz condition, where t is a positiveconstant.