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A Unified Derivative-Free Projection Framework for Convex-Constrained Nonlinear Equations

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  • Abdulkarim Hassan Ibrahim

    (Emirates Aviation University
    Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria
    Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals)

  • Mohammed Alshahrani

    (Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals
    King Fahd University of Petroleum and Minerals)

  • Suliman Al-Homidan

    (Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals
    King Fahd University of Petroleum and Minerals)

Abstract

This paper presents a framework and a unified convergence analysis for derivative-free projection methods to solve large-scale constrained nonlinear equations. The framework combines the inertial extrapolation technique with the concept of approximate projections, thereby encompassing and generalising the results of previous studies. Additionally, we introduce a new function-based line search based on the stabilised Barzilai and Borwein method, as introduced by Burdakov et al. The framework further explores the impact of six distinct, well-known line search schemes on its overall performance. Through numerical experiments, we highlight the theoretical findings.

Suggested Citation

  • Abdulkarim Hassan Ibrahim & Mohammed Alshahrani & Suliman Al-Homidan, 2026. "A Unified Derivative-Free Projection Framework for Convex-Constrained Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-26, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02826-x
    DOI: 10.1007/s10957-025-02826-x
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    References listed on IDEAS

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    1. Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
    2. Yekini Shehu & Aviv Gibali & Simone Sagratella, 2020. "Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 877-894, March.
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