A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing

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....

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Bibliographic Details
Published in:Heliyon 2020-03, Vol.6 (3), p.e03466-e03466, Article e03466
Main Authors: Ibrahim, Abdulkarim Hassan, Kumam, Poom, Abubakar, Auwal Bala, Jirakitpuwapat, Wachirapong, Abubakar, Jamilu
Format: Article
Language:English
Subjects:
Applied mathematics
Compressive sensing
Computer science
Conjugate gradient method
Convex constraints
Projection method
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Summary: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 ℓ1-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. Applied mathematics; Computer science; Conjugate gradient method; Projection method; Convex constraints; Compressive sensing
ISSN:2405-8440
2405-8440
DOI:10.1016/j.heliyon.2020.e03466