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| 解变分不等式问题的QP-free方法 | |
| 引用本文： | 周岩,桂胜华,濮定国.解变分不等式问题的QP-free方法[J].同济大学学报(自然科学版),2007,35(6):839-844. |
| 作者姓名： | 周岩 桂胜华 濮定国 |
| 作者单位： | 1. 同济大学,数学系,上海,200092;青岛大学,管理科学与工程系,山东,青岛,266071 2. 上海第二工业大学,应用数学系,上海,201029 3. 同济大学,数学系,上海,200092 |
| 基金项目： | 国家自然科学基金;上海市教委资助项目 |
| 摘 要： | 提出一种新的QP-free方法解变分不等式问题.通过光滑化的Fischer-Burmeister函数,把变分不等式的KKT优化条件转换为一个简单的约束优化问题,并给出了解这个约束优化问题的迭代算法.这个方法的主要优点是：①能够解任意的变分不等式问题;②每步迭代只需解一个线性方程组;③算法是全局收敛的,在一定条件下是超线性收敛的.数值试验结果表明,这个算法是有效的. |
| 关 键 词： | 变分不等式问题 QP-free算法 KKT优化条件 |
| 文章编号： | 0253-374X（2007）06-0839-06 |
| 修稿时间： | 2005-09-20 |
QP-free Method for Variational Inequality Problems |
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| ZHOU Yan,GUI Shenghua,PU Dingguo.QP-free Method for Variational Inequality Problems[J].Journal of Tongji University(Natural Science),2007,35(6):839-844. | |
| Authors: | ZHOU Yan GUI Shenghua PU Dingguo |
| Institution: | 1. Department of Mathematics, Tongji University, Shanghai 200092, China; 2. Department of Management Science and Engineering, Qingdao University, Qingdao 266071 ,China; 3. Department of Applied Mathematics, Shanghai Second Polytechnic University, Shanghai 201029, China |
| Abstract: | A new QP-free method is proposed for the solution of variational inequalities problem.By the smoothing Fischer-Burmeister functions,a simple constrained optimization reformulation of the KKT optimality conditions is derived from variational inequalities.Based on the reformulation,an iterative method is presented. The main properties of this method are: It is well defined for an arbitrary variational inequalities problem;it has to solve just one linear system of equations at each iteration;it is globally convergent;and it is locally superlinerly convergent under certain conditions.Preliminary numerical results indicate that this method is quite promising. |
| Keywords: | variational inequality problem QP-free method KKT optimality conditions |
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