A note on quadratic convergence of a smoothing Newton algorithm for the LCP

The linear complementarity problem (LCP) is to find $(x,s)\in <!--\; ?\; -->{\mathfrak{R}}^n\times <!--\; \times \; -->{\mathfrak{R}}^n$ such that (x, s) ≥ 0, s = Mx + q, x ^T s = 0 with $M\in <!--\; ?\; -->{\mathfrak{R}}^{n\times <!--\; \times \; -->n}$ and $q\in {\Re }^n$ . The smoothing Newton algorithm is one of the most efficient methods for solving the LCP. To the best of our knowledge, the best local convergence results of the smoothing Newton algorithm for the LCP up to now were obtained by Huang et al. (Math Program 99:423–441, 2004). In this note, by using a revised Chen–Harker–Kanzow–Smale smoothing function, we propose a variation of Huang–Qi–Sun’s algorithm and show that the algorithm possesses better local convergence properties than those given in Huang et al. (Math Program 99:423–441, 2004).