A spectral conjugate gradient projection algorithm to solve the large-scale system of monotone nonlinear equations with application to compressed sensing. Issue 11 (2nd November 2022)

• Record Type: Journal Article
• Authors: Amini, Keyvan; Faramarzi, Parvaneh; Bahrami, Somayeh
• Is Part Of: International journal of computer mathematics. Volume 99:Issue 11(2022)
• Page Start: 2290
• Page End: 2307
• Publication Date: 2022-11-02
• Subjects: Nonlinear monotone equation systems -- spectral conjugate gradient method -- projection algorithm -- compressed sensing -- large-scale problems; 90C30 -- 93A15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2047180
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, a derivative-free spectral projection technique to solve a system of large-scale nonlinear monotone equations is presented. The primary motivation is to use the appropriate structure of spectral conjugate gradient directions in the projection algorithms. The new direction is derivative-free and requires a little storage and computation. So, it is an appropriate direction to use in large-scale projection algorithms. We prove the global convergence and R-linear convergence rate of the proposed algorithm under some suitable conditions. Numerical experiments show a promising behaviour of the proposed algorithm to deal with large-scale monotone equations. Additionally, as a practical application, we use the new method to solve the l 1 -norm regularization problems to reconstruct a sparse signal in compressed sensing.