Volume 5, Issue 2
A Regularization Semismooth Newton Method for $P_0$-NCPs with a Non-Monotone Line Search

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 186-204.

Published online: 2012-05

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• Abstract

In this paper, we propose a regularized version of the generalized NCP-function proposed by Hu, Huang and Chen [J. Comput. Appl. Math., 230 (2009), pp. 69-82]. Based on this regularized function, we propose a semismooth Newton method for solving nonlinear complementarity problems, where a non-monotone line search scheme is used. In particular, we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions. We test the proposed method by solving the test problems from MCPLIB. Numerical experiments indicate that this algorithm has better numerical performance in the case of $p=5$ and $\theta\in[0.25,075]$  than other cases.

• Keywords

Nonlinear complementarity problem, non-monotone line search, semismooth Newton method, global convergence, local superlinear convergence.

90C33, 65K10

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@Article{NMTMA-5-186, author = {}, title = {A Regularization Semismooth Newton Method for $P_0$-NCPs with a Non-Monotone Line Search}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {2}, pages = {186--204}, abstract = {

In this paper, we propose a regularized version of the generalized NCP-function proposed by Hu, Huang and Chen [J. Comput. Appl. Math., 230 (2009), pp. 69-82]. Based on this regularized function, we propose a semismooth Newton method for solving nonlinear complementarity problems, where a non-monotone line search scheme is used. In particular, we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions. We test the proposed method by solving the test problems from MCPLIB. Numerical experiments indicate that this algorithm has better numerical performance in the case of $p=5$ and $\theta\in[0.25,075]$  than other cases.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m10027}, url = {http://global-sci.org/intro/article_detail/nmtma/5934.html} }
TY - JOUR T1 - A Regularization Semismooth Newton Method for $P_0$-NCPs with a Non-Monotone Line Search JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 186 EP - 204 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m10027 UR - https://global-sci.org/intro/article_detail/nmtma/5934.html KW - Nonlinear complementarity problem, non-monotone line search, semismooth Newton method, global convergence, local superlinear convergence. AB -

In this paper, we propose a regularized version of the generalized NCP-function proposed by Hu, Huang and Chen [J. Comput. Appl. Math., 230 (2009), pp. 69-82]. Based on this regularized function, we propose a semismooth Newton method for solving nonlinear complementarity problems, where a non-monotone line search scheme is used. In particular, we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions. We test the proposed method by solving the test problems from MCPLIB. Numerical experiments indicate that this algorithm has better numerical performance in the case of $p=5$ and $\theta\in[0.25,075]$  than other cases.

Li-Yong Lu, Wei-Zhe Gu & Wei Wang. (2020). A Regularization Semismooth Newton Method for $P_0$-NCPs with a Non-Monotone Line Search. Numerical Mathematics: Theory, Methods and Applications. 5 (2). 186-204. doi:10.4208/nmtma.2012.m10027
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