Derivative-free SMR conjugate gradient method for constraint nonlinear equations

Abdulkarim Hassan Ibrahim, Kanikar Muangchoo*, Nur Syarafina Mohamed, Auwal Bala Abubakard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Based on the SMR conjugate gradient method for unconstrained optimization proposed by Mohamed et al. [N. S. Mohamed, M. Mamat, M. Rivaie, S. M. Shaharuddin, Indones. J. Electr. Eng. Comput. Sci., 11 (2018), 1188-1193] and the Solodov and Svaiter projection technique, we propose a derivative-free SMR method for solving nonlinear equations with convex constraints. The proposed method can be viewed as an extension of the SMR method for solving unconstrained optimization. The proposed method can be used to solve large-scale nonlinear equations with convex constraints because of derivative-free and low storage. Under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity assumption, we prove its global convergence. Preliminary numerical results show that the proposed method is promising.

Original languageEnglish
Pages (from-to)147-164
Number of pages18
JournalJournal of Mathematics and Computer Science
Issue number2
Publication statusPublished - 2022
Externally publishedYes


  • Conjugate gradient method
  • Global convergence
  • Nonlinear equations
  • Projection method


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