| 求解无限维非线性互补问题的光滑化牛顿法 |
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| 引用本文： | 刘晶,高岩.求解无限维非线性互补问题的光滑化牛顿法[J].数学的实践与认识,2010,40(13). |
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| 作者姓名： | 刘晶 高岩 |
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| 基金项目： | 国家自然科学基金，广东省自然科学基金资助，五邑大学博士科研启动基金 |
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| 摘 要： | 研究一类无限维非线性互补问题的光滑化牛顿法.借助于非线性互补函数,将无限维非线性互补问题转化为一个非光滑算子方程.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化牛顿法具有超线性收敛性.
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| 关 键 词： | 互补问题 非光滑算子方程 光滑化牛顿法 光滑化逼近 |
Smoothing Newton Method for Solving Infinite-Dimensional Nonlinear Complementarity Problem |
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| LIU Jing,GAO Yan.Smoothing Newton Method for Solving Infinite-Dimensional Nonlinear Complementarity Problem[J].Mathematics in Practice and Theory,2010,40(13). |
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| Authors: | LIU Jing GAO Yan |
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| Abstract: | The smoothing Newton method for solving an infinite-dimensional nonlinear complementarity problem is studied.By menas of a nonlinear complementarity function,an infinite-dimensional nonlinear complementarity problem is turned into the nonsmooth operator equations.The feature is to use a smooth function to approximate the nonsmooth operator. Under the conditions of a smooth approximation operator satisfying the directionally differentiable consistence property,the superlinearly convergence of the smoothing Newton method is proved. |
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| Keywords: | complementarity problem nonsmooth operator equations smoothing Newton method smoothing approximation |
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