@article{Ma2024, 
author = {Xuejie Ma and Songhua Wang},
title = {A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36167-36190},
keywords = {constrained nonlinear systems of equations, conjugate gradient method, large-scale, global convergence, signal reconstruction},
url = {https://www.sciopen.com/article/10.3934/math.20241717},
doi = {10.3934/math.20241717},
abstract = {This paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed algorithm presents several significant advancements and key features:  (i) the conjugate parameter is constructed by utilizing the hybrid technique;  (ii) the search direction, designed with the conjugate parameter, possesses sufficient descent and trust region properties without the need for a line search mechanism;  (iii) the global convergence is rigorously established under general assumptions, notably without the requirement of the Lipschitz continuity condition;  (vi) numerical experiments demonstrate the algorithm's efficiency, particularly in solving large-scale constrained nonlinear systems of equations and addressing the sparse signal restoration problem.}
}