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

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

内蒙古大学理工学院数学系, 呼和浩特 010021

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)

详细信息

作者简介:
乌力吉(1962- ),男,内蒙古赤峰人,副教授,硕士(联系人.联系地址:内蒙古工业大学理学院数学系,呼和浩特,010062;Tel:+86-471-6575425;Fax:+86-471-6575877;E-mail:Ulji@imut.edu.cn).

中图分类号: O211
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- 文章访问数: 2606
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出版历程
- 收稿日期: 2003-12-08
- 修回日期: 2005-03-10
- 刊出日期: 2005-08-15

New Simple Smooth Merit Function for Box Constrained Variational Inequalities and Damped Newton Type Method

Ulji,
CHEN Guo-qing

Department of Mathematics, College of Science and Technology, Inner Mongolia University, Hohhot 010021, P. R. China

摘要

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．
- 箱约束变分不等式 /
- 全局收敛 /
- 超线性收敛 /
- 有限步收敛
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.
- box constr ained variational inequality /
- global convergence /
- local superlinear or quadratic converg ence /
- finite termination property

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参考文献(14)

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[5]	乌力吉,陈国庆.非线性互补问题的一种新的光滑价值函数及牛顿类算法[J].计算数学，2004,26(3):315—328.
[6]	陈国庆,曹兵.箱式约束变分不等式的一种新NCP-函数及其广义牛顿法[J].计算数学,2002,24(1):91—104.
[7]	Gabriel S A,More J J.Smoothing of mixed complementarity problems[A].In:Ferris M C,Pang J S Eds.Complementarity and Variational Problems: State of the Art[C].Philadelphia:SIAM,1996,105—116.
[8]	SUN De-feng,Womersley R S.A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Guass-Newton method[J].SIAM J Optim,1999,9(2):388—413. doi: 10.1137/S1052623496314173
[9]	QI Li-qun,SUN De-feng,ZHOU Guang-lu.A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities[J].Math Programming,1999,87(1):1—35.
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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

作者简介:
乌力吉(1962- ),男,内蒙古赤峰人,副教授,硕士(联系人.联系地址:内蒙古工业大学理学院数学系,呼和浩特,010062;Tel:+86-471-6575425;Fax:+86-471-6575877;E-mail:Ulji@imut.edu.cn).

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New Simple Smooth Merit Function for Box Constrained Variational Inequalities and Damped Newton Type Method

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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

作者简介: 乌力吉(1962- ),男,内蒙古赤峰人,副教授,硕士(联系人.联系地址:内蒙古工业大学理学院数学系,呼和浩特,010062;Tel:+86-471-6575425;Fax:+86-471-6575877;E-mail:Ulji@imut.edu.cn).

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出版历程

New Simple Smooth Merit Function for Box Constrained Variational Inequalities and Damped Newton Type Method

计量

出版历程

目录

作者简介:
乌力吉(1962- ),男,内蒙古赤峰人,副教授,硕士(联系人.联系地址:内蒙古工业大学理学院数学系,呼和浩特,010062;Tel:+86-471-6575425;Fax:+86-471-6575877;E-mail:Ulji@imut.edu.cn).