A smoothing Newton algorithm for the LCP with a sufficient matrix that terminates finitely at a maximally complementary solution

Abstract

By using a smoothing function, the linear complementarity problem (LCP) can be reformulated as a parameterized smooth equation. A Newton method with a projection-type testing procedure is proposed to solve this equation. We show that, for the LCP with a sufficient matrix, the iteration sequence generated by the proposed algorithm is bounded as long as the LCP has a solution. This assumption is weaker than the ones used in most existing smoothing algorithms. Moreover, we show that the proposed algorithm can find a maximally complementary solution to the LCP in a finite number of iterations.