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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<inf>*</inf>(κ) complementarity problem, which is based on the wide-neighborhood N<sup>−</sup><inf>∞</inf>(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 over 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.