@article{Awwal2025, 
author = {Aliyu Muhammad Awwal and Sulaiman M. Ibrahim and Issam A. R. Moghrabi and Mahmoud M. Yahaya and Aishatu I. Ahmad and Semiu Oladipupo Oladejo and Karimov Javlon Kuzievich and Aceng Sambas},
title = {A matrix-free DFP-like optimization method for problems arising from compressive sensing},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {7},
pages = {4091-4118},
keywords = {three-term conjugate gradient algorithms, optimization models, global convergence, line search procedure, signal processing},
url = {https://www.sciopen.com/article/10.3934/era.2025183},
doi = {10.3934/era.2025183},
abstract = {This paper introduces a matrix-free variant of the Davidon-Fletcher-Powell (DFP) method for unconstrained optimization problems with applications in compressive sensing and image restoration. The main contribution lies in the new search direction incorporating a scaling parameter that ensures the satisfaction of the sufficient descent condition, independent of the line search conditions. A rigorous convergence analysis guarantees the boundedness and theoretical validity of the proposed method. Comprehensive numerical experiments on benchmark unconstrained optimization test problems and compressive sensing problems demonstrate the efficiency and robustness of the algorithm. Specifically, in image restoration tasks, our method outperforms CG-DESCENT, MDL, and NSMA, achieving a 100% success rate compared to 95.8%, 84.5%, and 53.5%, respectively. Additionally, results on computational time, relative error, and PSNR confirm the superior performance of the proposed approach. These findings establish the proposed method as a competitive alternative for large-scale optimization problems.}
}