信赖域方法在Hölderian局部误差界下的收敛性质

doi:10.12286/jssx.j2020-0692

计算数学 ›› 2021, Vol. 43 ›› Issue (4): 484-492.DOI: 10.12286/jssx.j2020-0692

信赖域方法在Hölderian局部误差界下的收敛性质

马积瑞, 范金燕

上海交通大学数学科学学院, 教育部科学工程计算重点实验室, 上海 200240

收稿日期:2020-05-11 出版日期:2021-11-14 发布日期:2021-11-12
通讯作者: 范金燕,jyfan@sjtu.edu.cn
基金资助:
国家自然科学基金（11971309）资助.

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马积瑞, 范金燕. 信赖域方法在Hölderian局部误差界下的收敛性质[J]. 计算数学, 2021, 43(4): 484-492.

Ma Jirui, Fan Jinyan. ON THE CONVERGENCE OF THE TRUST REGION METHOD UNDER THE HÖLDERIAN ERROR BOUND CONDITION[J]. Mathematica Numerica Sinica, 2021, 43(4): 484-492.

ON THE CONVERGENCE OF THE TRUST REGION METHOD UNDER THE HÖLDERIAN ERROR BOUND CONDITION

Ma Jirui, Fan Jinyan

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China; School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2020-05-11 Online:2021-11-14 Published:2021-11-12

信赖域方法是求解非线性方程组的一种重要方法.本文研究了求解非线性方程组的信赖域半径趋于零的信赖域算法在Jacobi矩阵Hölderian连续条件下的全局收敛性质，以及其在Hölderian局部误差界和Jacobi矩阵Hölderian连续条件下的收敛速度.

关键词： 非线性方程组, 信赖域方法, Hölderian局部误差界

The trust region method is an improtant method for solving nonlinear equations. In this paper, we study the global convergence of the trust region method with trust region converging to zero under the Hölderian continuousness of the Jacobian. The convergence rate of the method is also given under the Hölderian error bound condition.

Key words: nonlinear equations, trust region method, Hölderian continuousness, Hölderian local error bound

MR(2010)主题分类:

65K05
90C30

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信赖域方法在Hölderian局部误差界下的收敛性质

ON THE CONVERGENCE OF THE TRUST REGION METHOD UNDER THE HÖLDERIAN ERROR BOUND CONDITION

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