Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization

Wenqing Ouyang, Jiong Tao, Andre Milzarek, Bailin Deng

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

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.

Original languageEnglish
Article number5
JournalJournal of Scientific Computing
Volume96
Issue number1
DOIs
Publication statusPublished - 18 May 2023

Bibliographical note

Funding Information:
A. Milzarek was partly supported by the Fundamental Research Fund - Shenzhen Research Institute for Big Data (SRIBD) Startup Fund JCYJ-AM20190601. B. Deng was partly supported by the Guangdong International Science and Technology Cooperation Project (No. 2021A0505030009).

Data Availability:
The datasets generated during and/or analysed during the current study are available in the GitHub repository https://github.com/bldeng/Nonmonotone-AA.

Keywords

  • Adaptive regularization
  • Anderson acceleration
  • Global convergence
  • Nonmonotone trust region

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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