Solving nonlinear monotone operator equations via modified SR1 update

Auwal Bala Abubakar, Jamilu Sabi’u, Poom Kumam*, Abdullah Shah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms were established under suitable assumptions on the operator under consideration. In addition, numerical experiments were conducted on some benchmark test problems to depict the efficiency and competitiveness of the algorithms compared with existing algorithms. From the results of the experiments, we can conclude that the proposed algorithms are more efficient and robust.

Original languageEnglish
Pages (from-to)343-373
Number of pages31
JournalJournal of Applied Mathematics and Computing
Issue number1-2
Publication statusPublished - Oct 2021
Externally publishedYes


  • Derivative-free method
  • Nonlinear monotone operator equations
  • Self-scaling memoryless SR1 update


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