Nonmonotone globalization for Anderson acceleration via adaptive regularization

Ouyang, Wenqing, Tao, Jiong, Milzarek, Andre and Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 2023. Nonmonotone globalization for Anderson acceleration via adaptive regularization. Journal of Scientific Computing 96 (5) 10.1007/s10915-023-02231-4

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Abstract

Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local convergence. Unlike existing AA globalization approaches that rely on safeguarding operations and might hinder fast local convergence, we adopt a nonmonotone trust-region framework and introduce an adaptive quadratic regularization together with a tailored acceptance mechanism. We prove global convergence and show that our algorithm attains the same local convergence as AA under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics
ISSN:	0885-7474
Date of First Compliant Deposit:	12 May 2023
Date of Acceptance:	29 April 2023
Last Modified:	19 May 2023 09:16
URI:	https://orca.cardiff.ac.uk/id/eprint/159464

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