Anderson Acceleration of Derivative-Free Projection Methods for Constrained Monotone Nonlinear Equations

Jiachen Jin (), Hongxia Wang () and Kangkang Deng ()
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Jiachen Jin: National University of Defense Technology
Hongxia Wang: National University of Defense Technology
Kangkang Deng: National University of Defense Technology

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 37, 30 pages

Abstract: 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 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.

Keywords: Anderson acceleration; Derivative-free projection method; Monotone nonlinear equations; Convergence; 65K05; 90C56; 65H10 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02841-y

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