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| 混合互补问题的光滑算法及收敛性 | |
| 引用本文： | 何郁波,马昌凤,董晓亮. 混合互补问题的光滑算法及收敛性[J]. 经济数学, 2010, 27(3): 73-78 |
| 作者姓名： | 何郁波 马昌凤 董晓亮 |
| 作者单位： | 1. 怀化学院,数学系,湖南,怀化,418008 2. 福建师范大学,数学与计算机科学学院,福建,福州,321004 3. 北方民族大学,信息与计算科学学院,宁夏,银川,750021 |
| 基金项目： | 湖南省教育厅资助项目 |
| 摘 要： | 利用Fischer-Burmeister函数将混合互补问题转化为非线性方程组，由光滑函数逼近FB函数来求解非线性方程组．文中将信赖域方法和梯度法相结合，提出了Jacobian光滑化方法．算法在一定条件下的全局收敛性得到了证明，数值试验表明算法切实有效，有一定的优越性． |
| 关 键 词： | 混合互补问题 Jacobian光滑算法 信赖域方法 梯度步 全局收敛 二阶收敛 |
The Convergence of a Smoothing Method for the Mixed Complementarity Problem |
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| HE Yu bo,MA Chang feng and DONG Xiao liang. The Convergence of a Smoothing Method for the Mixed Complementarity Problem[J]. Mathematics in Economics, 2010, 27(3): 73-78 | |
| Authors: | HE Yu bo MA Chang feng DONG Xiao liang |
| Affiliation: | 1. Department of Mathematics and applied mathematics, Huaihua University,Huaihua,Huna 418008,China 2. School of mathematics and computer science j Fujian Normal University, Fuzhou,Fujia 350007 ,China ; 3. School of Information and computation science, the North University for Ethnics, Yinchuan ,Ning：ria 750021 ,China) |
| Abstract: | We converted the mixed complementarity problem into a system of nonsmooth nonlinear equations by using Fischer--Burmeister function, and we used a smooth function to approximate the Fischer- Burmeister function. By combining trust region method with gradient method, a Jacobian smoothing method was proposed. Under some conditions, we proved the global convergence and local convergence of the algorithm. Numerical result indicates that the algorithm is quite promising. |
| Keywords: | mixed complementarity problem Jacobian smoothing method trust region method gradient step global convergence quadratic convergence |
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