On Superlinear and Convergence of a Path-Following Algorithm for Monotone Linear Complementarity Problems in a Wide Neighborhood. (4th May 2017) - Ma, Xiaojue; Liu, Hongwei; Zhang, Jianke; Cong, Weijie
ABSTRACT: We propose a modified path-following algorithm in a wide neighborhood for monotone linear complementarity problems. The algorithm takes two steps in one iteration, called a fast step and a safe step, respectively. In the algorithm, if a fast step fails, a safe step will be taken. However, when iterations are suﬃciently large, fast steps are taken all through. We prove that the algorithm has not only the complexity bound but also local superlinear convergence. Furthermore, assuming a strictly complementary solution exists, the sequence, generated by the algorithm, is convergent. Finally, the numerical results show the algorithm effective.