Abstract:

In this paper, we study the method for solving the special weighted linear complementarity problem. Based on a weighted smoothing function, we reformulate the problem as a system of smooth nonlinear equations and then propose a predictor-corrector smoothing Newton method to solve it. Under some suitable conditions, we show that the algorithm has the global and local quadratic convergence properties. In particular, when the solution set is nonempty we show that the merit function sequence converges to zero. Numerical experiments demonstrate that our algorithm is effective.

Key words: Weighted linear complementary problem, Smoothing Newton method, Global convergence, Quadratic convergence