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Volume 29, Issue 3
A Smoothing Trust Region Method for NCPs Based on the Smoothing Generalized Fischer-Burmeister Function

Xuebin Wang, Changfeng Ma, & Meiyan Li

DOI: 10.4208/jcm.1009-m3216

J. Comp. Math., 29 (2011), pp. 261-286.

Published online: 2011-06

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  • Abstract

Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generalized Fischer-Burmeister function, a smoothing trust region algorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.

  • Keywords

Nonlinear complementarity problem, Smoothing method, Trust region method, Global convergence, Local superlinear convergence.

  • AMS Subject Headings

90C33, 90C30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-261, author = {Xuebin Wang, Changfeng Ma, and Meiyan Li}, title = {A Smoothing Trust Region Method for NCPs Based on the Smoothing Generalized Fischer-Burmeister Function}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {3}, pages = {261--286}, abstract = {

Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generalized Fischer-Burmeister function, a smoothing trust region algorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1009-m3216}, url = {http://global-sci.org/intro/article_detail/jcm/8478.html} }
TY - JOUR T1 - A Smoothing Trust Region Method for NCPs Based on the Smoothing Generalized Fischer-Burmeister Function AU - Xuebin Wang, Changfeng Ma, & Meiyan Li JO - Journal of Computational Mathematics VL - 3 SP - 261 EP - 286 PY - 2011 DA - 2011/06 SN - 29 DO - http://doi.org/10.4208/jcm.1009-m3216 UR - https://global-sci.org/intro/article_detail/jcm/8478.html KW - Nonlinear complementarity problem, Smoothing method, Trust region method, Global convergence, Local superlinear convergence. AB -

Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generalized Fischer-Burmeister function, a smoothing trust region algorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.

Xuebin Wang, Changfeng Ma, and Meiyan Li. (2011). A Smoothing Trust Region Method for NCPs Based on the Smoothing Generalized Fischer-Burmeister Function. Journal of Computational Mathematics. 29 (3). 261-286. doi:10.4208/jcm.1009-m3216
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