@article{Xia2025, 
author = {Yan Xia and Dandan Li},
title = {An inertial hybrid CGP-based algorithm with restart strategy for constrained nonlinear equations and impulse noise image restoration},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {23360-23379},
keywords = {nonlinear equations, conjugate gradient projection method, inertial-related scheme, theoretical analysis, impulse noise image restoration},
url = {https://www.sciopen.com/article/10.3934/math.20251037},
doi = {10.3934/math.20251037},
abstract = {The conjugate gradient method is widely recognized as one of the most efficient approaches for solving large-scale optimization problems. In this paper, we have propose a novel hybrid conjugate gradient projection (CGP)-based algorithm that integrates an improved conjugate coefficient derived from the Hestenes-Stiefel (HS) and Polak-Ribière-Polak (PRP) formulas. The proposed algorithm exhibits several key characteristics:  (ⅰ) The hybrid coefficient with a single parameter was employed to construct a search direction that ensures both the sufficient descent condition and trust-region feature, enhanced via a restart strategy;  (ⅱ) we incorporated an inertial-relaxed scheme alongside a projection technique in a hybrid CGP-based framework for further improving performance;  (ⅲ) we established the global convergence of the proposed algorithm under relaxed assumptions, providing a solid theoretical foundation; and (iv) extensive numerical experiments demonstrated the superior numerical performance of the proposed algorithm compared to existing algorithms on large-scale constrained nonlinear equations and impulse noise image restoration problems.}
}