Improving the convergence of non-interior point algorithms for nonlinear complementarity problems

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and th e trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity prob lem. Their algorithm is globally convergent under a relatively mild conditi on. In this paper, we modify their algorithm and combine it with the superl inear convergence theory for nonlinear equations. We provide a globally lin early convergent result for a slightly updated version of the Hotta-Yoshise algorithm and show that a further modified Hotta-Yoshise algorithm is glob ally and superlinearly convergent, with a convergence Q-order 1 + t, under suitable conditions, where t is an element of (0, 1) is an additional param eter.