On convergence properties of the modified trust region method under Hölderian error bound condition

Jirui Ma; Jinyan Fan

doi:10.3934/jimo.2021222

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2023, Volume 19, Issue 2: 1139-1151. Doi: 10.3934/jimo.2021222

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On convergence properties of the modified trust region method under Hölderian error bound condition

Jirui Ma^1, and
Jinyan Fan^2, ,

1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
2.
School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China

^* Corresponding author: Jinyan Fan
^* Corresponding author: Jinyan Fan

Received: April 30, 2021

Revised: August 31, 2021

Published: February 2023

The authors are supported by the National Natural Science Foundation of China grant 11971309

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Abstract

Trust region method is one of the important methods for nonlinear equations. In this paper, we show that the modified trust region method converges globally under the Hölderian continuity of the Jacobian. The convergence order of the method is also given under the Hölderian error bound condition.

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Mathematics Subject Classification: 65K05, 65K10, 90C26, 90C30.

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