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

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.