Numerical comparisons of two effective methods for mixed complementarity problems

Authors:
Jein-Shan Chen;Shaohua Pan;Ching-Yu Yang
Affiliations:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677, Taiwan;School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China;Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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 p-norm (p1) for the two methods and investigate how much the improvement is by changing the parameter p 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 p on MCPLIB collection.