Numerical comparisons of two effective methods for mixed complementarity problems

Recently there have two different effective methods proposed by Kanzow et al. in (Kanzow, 2001 [8]) and (Kanzow and Petra, 2004 [9]), respectively, which commonly use the Fischer–Burmeister (FB) function to recast the mixed complementarity problem (MCP) as a constrained minimization problem and a nonlinear system of equations, respectively. They all remark that their algorithms may be improved if the FB function is replaced by other NCP functions. Accordingly, in this paper, we employ the generalized Fischer–Burmeister (GFB) where the 2-norm in the FB function is relaxed to a general pp-norm (p>1p>1) for the two methods and investigate how much the improvement is by changing the parameter pp as well as which method is influenced more when we do so, by the performance profiles of iterations and function evaluations for the two methods with different pp on MCPLIB collection.