| Banach空间中非光滑算子方程的光滑化拟牛顿法 |
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| 引用本文： | 孙立兵,刘晶,宋文.Banach空间中非光滑算子方程的光滑化拟牛顿法[J].数学的实践与认识,2008,38(13). |
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| 作者姓名： | 孙立兵 刘晶 宋文 |
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| 作者单位： | 1. 哈尔滨师范大学,数学系,黑龙江,哈尔滨,150080
2. 五邑大学,数学物理系,广东,江门,529020 |
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| 基金项目： | 国家自然科学基金，黑龙江省自然科学基金，黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 研究Banach空间中非光滑算子方程的光滑化拟牛顿法.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,证明了光滑化拟牛顿法具有局部超线性收敛性质.应用说明了算法的有效性.
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| 关 键 词： | 非光滑算子方程 光滑化拟牛顿法 光滑逼近算子 方向可微相容性 |
Smoothing quasi-Newton Method for Nonsmooth Operator Equations in Banach Spaces |
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| SUN Li-bing,LIU Jing,SONG Wen.Smoothing quasi-Newton Method for Nonsmooth Operator Equations in Banach Spaces[J].Mathematics in Practice and Theory,2008,38(13). |
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| Authors: | SUN Li-bing LIU Jing SONG Wen |
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| Abstract: | The smoothing quasi-Newton method for solving nonsmooth operator equations in Banach spaces is studied.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 locally superlinearly convergence of the smoothing quasi-Newton method is proved.The application of the algorithm shows that it is valid. |
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| Keywords: | nonsmooth operator equations smoothing quasi-Newton method smooth approximation operator the directionally differentiable consistence property |
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