TY - JOUR
T1 - A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs
AU - Chen, Jein-Shan
AU - Pan, Shaohua
AU - Lin, Tzu Ching
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 - 2010/5/1
Y1 - 2010/5/1
N2 - We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ (1, 2] has better numerical performance than the one with p > 2.
AB - We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ (1, 2] has better numerical performance than the one with p > 2.
KW - Convergence rate
KW - Mixed complementarity problem
KW - Smoothing approximation
KW - The generalized FB function
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U2 - 10.1016/j.na.2010.01.012
DO - 10.1016/j.na.2010.01.012
M3 - Article
AN - SCOPUS:76549123306
VL - 72
SP - 3739
EP - 3758
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 9-10
ER -