A hybrid BFGS-Like method for monotone operator equations with applications

A. B. Abubakar, P. Kumam*, H. Mohammad, A. H. Ibrahim, T. Seangwattana, B. A. Hassan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, a hybrid three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is computed such that it is close to the direction obtained by the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) method. Without any condition, the search direction is sufficiently descent and bounded. Moreover, based on some conditions, the search direction satisfy the conjugacy condition without using any line search. The global convergence of the method is established under mild assumptions. Comparison with existing methods is done to test the efficiency of the proposed method through some numerical experiments. Lastly, the applicability of the proposed method is shown.

Original languageEnglish
Article number115857
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 15 Aug 2024
Externally publishedYes


  • Conjugate gradient
  • Global convergence
  • Non-linear equations
  • Projection map


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