Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

Jamilu Sabi’u, Kazeem Olalekan Aremu, Ali Althobaiti, Abdullah Shah

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Martínez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving largescale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.

Original languageEnglish
Article number936
Issue number5
Publication statusPublished - May 2022
Externally publishedYes


  • constrained monotone system
  • descent condition
  • projection technique
  • scaled three-term CG method


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