A wide-neighborhood interior-point method for P*(κ) complementarity problem

In this paper we propose a new potential reduction interior-point method for a kind of nonlinear nonmonotone complementarity problem-P_*(κ) complementarity problem, which is based on the wide-neighborhood N_∞^-(β). This method is a generalization of Mizuno, Todd and Ye´s result. Although the search direction of this algorithm 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((2κ + 1 + max{κ, 1/4}M)nt) is attained when the problem satisfies a scaled Lipschitz condition, where t is a positive constant and M is defined in the condition.