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

Abdulkarim Hassan Ibrahim (), Mohammed Alshahrani () and Suliman Al-Homidan ()
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Abdulkarim Hassan Ibrahim: Emirates Aviation University
Mohammed Alshahrani: Interdisciplinary Research Center for Smart Mobility and Logistics, 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

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 11, 26 pages

Abstract: 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.

Keywords: Iterative method; Nonlinear equations; Large-scale systems; Projection method; 47J05; 47J25 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02826-x

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