A full-Newton step non-interior continuation algorithm for a class of complementarity problems

In this paper, we investigate a class of nonlinear complementarity problems arising from the discretization of the free boundary problem, which was recently studied by Sun and Zeng [Z. Sun, J. Zeng, A monotone semismooth Newton type method for a class of complementarity problems, J. Comput. Appl. Math. 235 (5) (2011) 1261–1274]. We propose a new non-interior continuation algorithm for solving this class of problems, where the full-Newton step is used in each iteration. We show that the algorithm is globally convergent, where the iteration sequence of the variable converges monotonically. We also prove that the algorithm is globally linearly and locally superlinearly convergent without any additional assumption, and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate the effectiveness of the proposed algorithm.