Predictor-Corrector Smoothing Methods for Monotone LCP

Abstract In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in 1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in 1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in 1]. In addition, the difference between Algorithm 2.1 and the algorithm in 1] exists in the calculation of the predictor step. Comparing with the results in 1], the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1′ is obtained under the assumption of nonsingularity of generalized Jacobian of φ(x, y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The effciency of the two methods is tested by numerical experiments. Supported in part by the National Science Foundation of China (No.70302003, 10171055) and by China Postdoctoral Science Foundation.