A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

Abdulkarim Hassan Ibrahim, Poom Kumam*, Basim A. Hassan, Auwal Bala Abubakar, Jamilu Abubakar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

Original languageEnglish
JournalInternational Journal of Computer Mathematics
DOIs
Publication statusAccepted/In press - 2021
Externally publishedYes

Keywords

  • 65K05
  • 65L09
  • 90C30
  • compressive sensing
  • conjugate gradient method
  • derivative-free method
  • nonlinear equations
  • projection method
  • Unconstrained optimization

Fingerprint

Dive into the research topics of 'A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration'. Together they form a unique fingerprint.

Cite this