Locating a maximally complementary solution of the monotone NCP by using non-interior-point smoothing algorithms

Abstract.

In this paper we propose a non-interior-point smoothing algorithm for solving the monotone nonlinear complementarity problem (NCP). The proposed algorithm is simpler than many existing non-interior-point smoothing algorithms in the sense that it only needs to solve one system of linear equations and to perform one line search at each iteration. We show that the proposed algorithm is globally convergent under the assumption that the NCP concerned has a nonempty solution set. Such assumption is weaker than those required by most other non-interior-point smoothing algorithms. In particular, we prove that the solution obtained by the proposed algorithm is a maximally complementary solution of the NCP concerned. Preliminary numerical results are reported.