Volume 24, Issue 1
A LQP Based Interior Prediction-Correction Method for Nonlinear Complementarity Problems

Bing-sheng He, Li-zhi Liao & Xiao-ming Yuan

DOI:

J. Comp. Math., 24 (2006), pp. 33-44

Published online: 2006-02

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  • Abstract

To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system of nonlinear equations ({\it LQP system}). This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the {\it LQP system} approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.

  • Keywords

Logarithmic-Quadratic proximal method Nonlinear complementarity problems Prediction-correction Inexact criterion

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@Article{JCM-24-33, author = {}, title = {A LQP Based Interior Prediction-Correction Method for Nonlinear Complementarity Problems}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {1}, pages = {33--44}, abstract = { To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system of nonlinear equations ({\it LQP system}). This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the {\it LQP system} approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8732.html} }
TY - JOUR T1 - A LQP Based Interior Prediction-Correction Method for Nonlinear Complementarity Problems JO - Journal of Computational Mathematics VL - 1 SP - 33 EP - 44 PY - 2006 DA - 2006/02 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8732.html KW - Logarithmic-Quadratic proximal method KW - Nonlinear complementarity problems KW - Prediction-correction KW - Inexact criterion AB - To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system of nonlinear equations ({\it LQP system}). This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the {\it LQP system} approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
Bing-sheng He, Li-zhi Liao & Xiao-ming Yuan. (1970). A LQP Based Interior Prediction-Correction Method for Nonlinear Complementarity Problems. Journal of Computational Mathematics. 24 (1). 33-44. doi:
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