PRP-like algorithm for monotone operator equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the ℓ1-norm regularized minimization problem.

Original languageEnglish
Pages (from-to)805-822
Number of pages18
JournalJapan Journal of Industrial and Applied Mathematics
Volume38
Issue number3
DOIs
Publication statusPublished - Sep 2021
Externally publishedYes

Keywords

  • Conjugate gradient
  • Image restoration
  • Nonlinear equations
  • Projection method

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