Inexact fixed-point iteration method for nonlinear complementarity problems

Abstract

Based on the modulus decomposition, the structured nonlinear complementarity problem is reformulated as an implicit fixed-point system of nonlinear equations. Distinguishing from some existing modulus-based matrix splitting methods, we present a flexible modulus-based inexact fixed-point iteration method for the resulting system, in which the subproblem can be solved approximately by a linear system-solver. The global convergence of the proposed method is established by assuming that the system matrix is positive definite. Some numerical comparisons are reported to illustrate the applicability of the proposed method, especially for large-scale problems.