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arXiv · 2403.14924

Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations

Jiachen Jin·Hongxia Wang·Kangkang Deng
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Abstract

The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application of Anderson acceleration (AA) to DFPM for constrained monotone nonlinear equations. By employing a nonstationary relaxation parameter and interleaving with slight modifications in each iteration, a globally convergent variant of AA for DFPM named as AA-DFPM is proposed. Further, the linear convergence rate is proved under some mild assumptions. Experiments on both mathematical examples and a real-world application show encouraging results of AA-DFPM and confirm the suitability of AA for accelerating DFPM in solving optimization problems.

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Jiachen Jin, Hongxia Wang, Kangkang Deng. 2024-03-22. Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations. https://doi.org/10.1007/s10957-025-02841-y

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