Ibrahim Abdulkarim Hassan, Kumam Poom, Abubakar Auwal Bala, Jirakitpuwapat Wachirapong, Abubakar Jamilu
KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
Heliyon. 2020 Mar 2;6(3):e03466. doi: 10.1016/j.heliyon.2020.e03466. eCollection 2020 Mar.
Combining the projection method of Solodov and Svaiter with the Liu-Storey and Fletcher Reeves conjugate gradient algorithm of Djordjević for unconstrained minimization problems, a hybrid conjugate gradient algorithm is proposed and extended to solve convex constrained nonlinear monotone equations. Under some suitable conditions, the global convergence result of the proposed method is established. Furthermore, the proposed method is applied to solve the -norm regularized problems to restore sparse signal and image in compressive sensing. Numerical comparisons of the proposed algorithm versus some other conjugate gradient algorithms on a set of benchmark test problems, sparse signal reconstruction and image restoration in compressive sensing show that the proposed scheme is computationally more efficient and robust than the compared schemes.
将索洛多夫和斯韦特的投影方法与乔尔杰维奇用于无约束极小化问题的刘-斯托里和弗莱彻-里夫斯共轭梯度算法相结合，提出并扩展了一种混合共轭梯度算法，用于求解凸约束非线性单调方程。在一些合适的条件下，建立了该方法的全局收敛结果。此外，将该方法应用于求解 -范数正则化问题，以在压缩感知中恢复稀疏信号和图像。在一组基准测试问题、压缩感知中的稀疏信号重建和图像恢复方面，将该算法与其他一些共轭梯度算法进行数值比较，结果表明，与比较方案相比，该方案在计算上更高效、更稳健。
