TY - JOUR
T1 - Numerical comparisons of two effective methods for mixed complementarity problems
AU - Chen, Jein Shan
AU - Pan, Shaohua
AU - Yang, Ching Yu
N1 - Funding Information:
The first author’s work is partially supported by National Science Council of Taiwan. The second author’s work is supported by National Young Natural Science Foundation (No. 10901058) and Guangdong Natural Science Foundation (No. 9251802902000001).
PY - 2010/6/1
Y1 - 2010/6/1
N2 - 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 (p > 1) 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.
AB - 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 (p > 1) 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.
KW - Convergence rate
KW - MCP
KW - Semismooth
KW - The generalized FB function
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U2 - 10.1016/j.cam.2010.01.004
DO - 10.1016/j.cam.2010.01.004
M3 - Article
AN - SCOPUS:77949486393
SN - 0377-0427
VL - 234
SP - 667
EP - 683
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 3
ER -