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

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence theory for nonlinear equations. We provide a globally linearly convergent result for a slightly updated version of the HottaYoshise algorithm and show that a further modified Hotta-Yoshise algorithm is globally and superlinearly convergent, with a convergence Q-order 1 + t, under suitable conditions, where t (0, 1) is an additional parameter.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Liqun Qi, Defeng Sun
• Keywords: Algorithm, MOC 2000, Noninterior Point Algorithm, Nonlinear Complementarity Problem