Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems

Muhammad Abdullahi*, Auwal Bala Abubakar, Sadiq Bashir Salihu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The conjugate gradient method (CG) is one of the most rapidly expanding and efficient ways of solving unconstrained minimization problems. Recently, there has been a lot of effort put into extending the CG approach to solve monotone nonlinear equations. In this paper, we describe a variation of the CG method for solving constrained monotone nonlinear equations. The approach has a sufficient descent property, and its global convergence has been demonstrated with the help of some reasonable assumptions. Two sets of numerical tests were run to demonstrate the proposed method's superior performance when compared to other methods. The initial experiment aimed to solve nonlinear equations with constraints, while in the second experiment, the method was applied to sparse signal reconstruction.

Original languageEnglish
Pages (from-to)2561-2584
Number of pages24
JournalRAIRO - Operations Research
Volume57
Issue number5
DOIs
Publication statusPublished - 1 Sept 2023
Externally publishedYes

Keywords

  • Convex constraint
  • Global convergence
  • Non-linear equations
  • Projection map
  • Signal processing

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