| 箱约束变分不等式的一个简单光滑价值函数和阻尼牛顿法 |
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| 引用本文： | 乌力吉,陈国庆.箱约束变分不等式的一个简单光滑价值函数和阻尼牛顿法[J].应用数学和力学,2005,26(8):988-996. |
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| 作者姓名： | 乌力吉 陈国庆 |
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| 作者单位： | 内蒙古大学,理工学院,数学系,呼和浩特,010021 |
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| 基金项目： | 高等学校优秀青年教师教学科研奖励计划资助项目(教人司[2002]123号) |
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| 摘 要： | 通过引入中间值函数的一类光滑价值函数,构造了箱约束变分不等式的一种新的光滑价值函数,该函数形式简单且具有良好的微分性质.基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法,在较弱的条件下,证明了算法的全局收敛性和局部超线性收敛率,以及对线性箱约束变分不等式的有限步收敛性.数值实验结果表明了算法可靠有效的实用性能.
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| 关 键 词： | 箱约束变分不等式 全局收敛 超线性收敛 有限步收敛 |
| 文章编号： | 1000-0887(2005)08-0988-09 |
| 修稿时间： | 2003年12月8日 |
New Simple Smooth Merit Function for Box Constrained Variational Inequalities and Damped Newton Type Method |
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| Ulji,CHEN Guo-qing.New Simple Smooth Merit Function for Box Constrained Variational Inequalities and Damped Newton Type Method[J].Applied Mathematics and Mechanics,2005,26(8):988-996. |
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| Authors: | Ulji CHEN Guo-qing |
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| Abstract: | By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising. |
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| Keywords: | box constrained variational inequality global convergence local superlinear or quadratic convergence finite termination property |
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