A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems

Aliyu Yusuf (), Nibron Haggai Manjak (), Hassan Mohammad (), Aliyu Ibrahim Kiri () and Auwal Bala Abubakar ()
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Aliyu Yusuf: Bayero University Kano
Nibron Haggai Manjak: Abubakar Tafawa Balewa University Bauchi
Hassan Mohammad: Bayero University Kano
Aliyu Ibrahim Kiri: Bayero University Kano
Auwal Bala Abubakar: Bayero University Kano

SN Operations Research Forum, 2024, vol. 5, issue 2, 1-16

Abstract: Abstract In this paper, we propose a method via hybrid spectral conjugate gradient to solve nonlinear monotone equations and signal recovery problems. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm are explored.

Keywords: Conjugate gradient method; Spectral gradient parameter; Nonlinear monotone equations; Global convergence; Numerical experiments (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s43069-024-00326-8

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