A hybrid approach for finding approximate solutions to constrained nonlinear monotone operator equations with applications

Auwal Bala Abubakar, Poom Kumam*, Hassan Mohammad, Abdulkarim Hassan Ibrahim, Aliyu Ibrahim Kiri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, a hybrid approach technique incorporated with three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is defined such that it is close to the one obtained by the memoryless Broyden-Fletcher-Goldferb-Shanno (BFGS) method. Independent of the line search, the search direction possesses the sufficient descent and trust region properties. Furthermore, the sequence of iterates generated converge globally under some appropriate assumptions. In addition, numerical experiments are carried out to test the efficiency of the proposed method in contrast with existing methods. Finally, the applicability of the proposed method in compressive sensing is shown.

Original languageEnglish
Pages (from-to)79-92
Number of pages14
JournalApplied Numerical Mathematics
Volume177
DOIs
Publication statusPublished - Jul 2022
Externally publishedYes

Keywords

  • Compressed sensing
  • Derivative-free projection method
  • Global convergence
  • Monotone operator equations

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