Another hybrid approach for solving monotone operator equations and application to signal processing. (19th April 2022)

• Record Type: Journal Article
• Authors: Kumam, Poom; Abubakar, Auwal Bala; Ibrahim, Abdulkarim Hassan; Kura, Hamza Umar; Panyanak, Bancha; Pakkaranang, Nuttapol
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 12(2022)
• Page Start: 7897
• Page End: 7922
• Publication Date: 2022-04-19
• Subjects: compressive sensing -- global convergence -- gradient method -- projection method -- signal reconstruction -- ℓ1$$ {\ell}_1 $$‐norm minimization; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8285
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.