Banach空间中非光滑算子方程的光滑化拟牛顿法  

Smoothing quasi-Newton Method for Nonsmooth Operator Equations in Banach Spaces

作　　者：孙立兵[1] 刘晶[2] 宋文[1] 

机构地区：[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

出　　处：《数学的实践与认识》2008年第13期192-199,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助项目(10671126);黑龙江省自然科学基金资助项目(A200607);黑龙江省教育厅科学技术研究资助项目(1151113710551108)

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.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.

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 

分 类 号：O177.2[理学—数学] O242.23[理学—基础数学]