### Abstract

We consider a regularization method for nonlinear complementarity problems with F being a P_{0}-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 φ_{p} 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 φ_{p} with p ∈ [1.1, 2) can be used as the substitutions for the FB function φ_{2}.

Original language | English |
---|---|

Pages (from-to) | 464-479 |

Number of pages | 16 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 220 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2008 Oct 15 |

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### Keywords

- Generalized Fischer-Burmeister function
- Nonlinear complementarity problem (NCP)
- P-function
- Semismooth Newton method

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

**A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P _{0}-NCPs.** / Chen, Jein-Shan; Pan, Shaohua.

Research output: Contribution to journal › Article

_{0}-NCPs',

*Journal of Computational and Applied Mathematics*, vol. 220, no. 1-2, pp. 464-479. https://doi.org/10.1016/j.cam.2007.08.020

}

TY - JOUR

T1 - A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs

AU - Chen, Jein-Shan

AU - Pan, Shaohua

PY - 2008/10/15

Y1 - 2008/10/15

N2 - 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.

AB - 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.

KW - Generalized Fischer-Burmeister function

KW - Nonlinear complementarity problem (NCP)

KW - P-function

KW - Semismooth Newton method

UR - http://www.scopus.com/inward/record.url?scp=47849106790&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=47849106790&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2007.08.020

DO - 10.1016/j.cam.2007.08.020

M3 - Article

AN - SCOPUS:47849106790

VL - 220

SP - 464

EP - 479

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -