求解非光滑方程组的三次正则化方法

doi:10.15960/j.cnki.issn.1007-6093.2019.02.002

运筹学学报 ›› 2019, Vol. 23 ›› Issue (2): 17-30.doi: 10.15960/j.cnki.issn.1007-6093.2019.02.002

求解非光滑方程组的三次正则化方法

苗小楠¹, 顾剑^2,*, 肖现涛¹

1. 大连理工大学数学科学学院, 辽宁大连 116024;
2. 大连海洋大学理学院, 辽宁大连 116024

收稿日期:2017-03-24 出版日期:2019-06-15 发布日期:2019-06-15
通讯作者: 顾剑 E-mail:gujian@dlou.edu.cn
基金资助:
国家自然科学基金（Nos.11871135，11801054）

A cubic regularization method for solving nonsmooth equations

MIAO Xiaonan¹, GU Jian^2,*, XIAO Xiantao¹

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China;
2. School of Sciences, Dalian Ocean University, Dalian 116024, Liaoning, China

Received:2017-03-24 Online:2019-06-15 Published:2019-06-15

摘要/Abstract

摘要： 考虑求解非光滑方程组的三次正则化方法及其收敛性分析.利用信赖域方法的技巧，保证该方法是全局收敛的.在子问题非精确求解和BD正则性条件成立的前提下，分析了非光滑三次正则化方法的局部收敛速度.最后，数值实验结果验证了该算法的有效性.

关键词: 三次正则化方法, 非光滑方程组, 局部收敛速度

Abstract: A cubic regularization method and its convergence for solving a nonsmooth system of equations are studied in this paper. By applying the classical trust region technique, the proposed method is ensured to be globally convergent. When BDregular condition is satisfied and the subproblem is inexactly solved, we analyze the local convergence rate of the nonsmooth cubic regularization method. Finally, the efficiency of our method is verified by numerical results.

Key words: cubic regularization method, nonsmooth equations, local convergence

中图分类号:

O221.2
O224

苗小楠, 顾剑, 肖现涛. 求解非光滑方程组的三次正则化方法[J]. 运筹学学报, 2019, 23(2): 17-30.

MIAO Xiaonan, GU Jian, XIAO Xiantao. A cubic regularization method for solving nonsmooth equations[J]. Operations Research Transactions, 2019, 23(2): 17-30.

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求解非光滑方程组的三次正则化方法

A cubic regularization method for solving nonsmooth equations

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