Volume 18, Issue 3
A Globally Derivative-Free Descent Method for Nonlinear Complementarity Problems

J. Comp. Math., 18 (2000), pp. 251-264.

Published online: 2000-06

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• Abstract

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free descent method in monotone case. We show its global convergence under some mild conditions. If $F$, the function involved in NCP, is $R_0$-function, the optimization problems has bounded level sets. A local property of the merit function is discussed. Finally,we report some numerical results.

• Keywords

Complementarity problem, NCP-function, unconstrained minimization method, derivative-free, descent method.

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@Article{JCM-18-251, author = {Qi , Huo-Duo and Zhang , Yu-Zhong}, title = {A Globally Derivative-Free Descent Method for Nonlinear Complementarity Problems}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {3}, pages = {251--264}, abstract = {

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free descent method in monotone case. We show its global convergence under some mild conditions. If $F$, the function involved in NCP, is $R_0$-function, the optimization problems has bounded level sets. A local property of the merit function is discussed. Finally,we report some numerical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9039.html} }
TY - JOUR T1 - A Globally Derivative-Free Descent Method for Nonlinear Complementarity Problems AU - Qi , Huo-Duo AU - Zhang , Yu-Zhong JO - Journal of Computational Mathematics VL - 3 SP - 251 EP - 264 PY - 2000 DA - 2000/06 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9039.html KW - Complementarity problem, NCP-function, unconstrained minimization method, derivative-free, descent method. AB -

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free descent method in monotone case. We show its global convergence under some mild conditions. If $F$, the function involved in NCP, is $R_0$-function, the optimization problems has bounded level sets. A local property of the merit function is discussed. Finally,we report some numerical results.

Huo-Duo Qi & Yu-Zhong Zhang. (1970). A Globally Derivative-Free Descent Method for Nonlinear Complementarity Problems. Journal of Computational Mathematics. 18 (3). 251-264. doi:
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