A three-term Polak-Ribière-Polyak derivative-free method and its application to image restoration

Abdulkarim Hassan Ibrahim, Jitsupa Deepho*, Auwal Bala Abubakar, Abubakar Adamu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, a derivative-free method for solving convex constrained nonlinear equations involving a monotone operator with a Lipschitz condition imposed on the underlying operator is introduced and studied. The proposed method incorporates the projection technique of Solodov and Svaiter with the three-term Polak-Ribière-Polyak conjugate gradient method for the unconstrained optimization problem proposed by Min Li [J. Ind. Manag. Optim.16.1(2020): 245.16.1 (2020): 245]. Under some standard assumptions, we establish the global convergence of the proposed method. Furthermore, we provide some numerical examples and application to image deblurring problem to illustrate the effectiveness and competitiveness of the proposed method. The numerical results indicate that the proposed method is remarkably promising.

Original languageEnglish
Article numbere00880
JournalScientific African
Volume13
DOIs
Publication statusPublished - Sep 2021
Externally publishedYes

Keywords

  • Derivative-free method
  • Global convergence
  • Image restoration
  • Nonlinear equations
  • Projection method

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