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

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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)

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.

Suggested Citation

  • Jiachen Jin & Hongxia Wang & Kangkang Deng, 2026. "Anderson Acceleration of Derivative-Free Projection Methods for Constrained Monotone Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-30, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02841-y
    DOI: 10.1007/s10957-025-02841-y
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