非光滑牛顿算法的收敛性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1537-1550.

非光滑牛顿算法的收敛性

许文丁(),钟婷*()

^{四川旅游学院大数据与统计学院成都 610100}

收稿日期:2021-10-14 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 钟婷 E-mail:wd-xu@hotmail.com;zhongting89@sina.cn
作者简介:许文丁, E-mail: wd-xu@hotmail.com
基金资助:
国家自然科学基金(11901414);四川旅游学院旅游统计与应用数学科研创新团队(20SCTUTY01)

The Convergence of Nonsmooth Newton's Method

Wending Xu(),Ting Zhong*()

^{College of Big Data and Statistics, Sichuan Tourism University, Chengdu 610100}

Received:2021-10-14 Online:2022-10-26 Published:2022-09-30
Contact: Ting Zhong E-mail:wd-xu@hotmail.com;zhongting89@sina.cn
Supported by:
the NSFC(11901414);the Foundation of Sichuan Tourism University(20SCTUTY01)

摘要/Abstract

摘要：

该文研究了求解包含问题的非光滑牛顿算法的收敛性. 运用度量正则性条件, 证明了非光滑牛顿算法的一个局部收敛性结果, 该结果通过利用非紧性测度, 削弱了已有相关结果的假设条件. 此外, 得到了非光滑牛顿算法的一个全局情形的收敛性结果, 即所需条件均假设于算法的初始点而非包含问题的解点.

关键词: 非光滑牛顿算法, 度量正则性, 收敛性, 非紧性测度

Abstract:

This paper studies the convergence of nonsmooth Newton's method for generalized inclusions. By applying metric regularity, a local convergence result of nonsmooth Newton's method is proved. The compactness in a known result is weakened through the measure of non-compactness. A convergence result in global version is established in which the conditions are assumed at the initial point while not the solution of the generalized inclusions.

Key words: Nonsmooth Newton's method, Metric regularity, Convergence, Measure of non-compactness

中图分类号:

O224

许文丁,钟婷. 非光滑牛顿算法的收敛性[J]. 数学物理学报, 2022, 42(5): 1537-1550.

Wending Xu,Ting Zhong. The Convergence of Nonsmooth Newton's Method[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1537-1550.

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