A regularization semismooth Newton method based on the generalized Fischer–Burmeister function for -NCPs |
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Authors: | Jein-Shan Chen Shaohua Pan |
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Institution: | aDepartment of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;bSchool of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China |
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Abstract: | We consider a regularization method for nonlinear complementarity problems with F being a P0-function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed by the generalized Fischer–Burmeister (FB) NCP-functions φp with p>1. We test the performance of the regularization semismooth Newton method based on the family of NCP-functions through solving all test problems from MCPLIB. Numerical experiments indicate that the method associated with a smaller p, for example p 1.1,2], usually has better numerical performance, and the generalized FB functions φp with p 1.1,2) can be used as the substitutions for the FB function φ2. |
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Keywords: | Nonlinear complementarity problem (NCP) Generalized Fischer– Burmeister function color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TYH-4PKXBR7-2&_mathId=mml37&_user=10&_cdi=5619&_rdoc=39&_acct=C000053510&_version=1&_userid=1524097&md5=7b0a27406fa8cd3aef0d987986945d24" title="Click to view the MathML source" P0-function" target="_blank">alt="Click to view the MathML source">P0-function Semismooth Newton method |
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