Comment on: “A derivative-free iterative method for nonlinear monotone equations with convex constraints”

Muhammad Abdullahi, Auwal Bala Abubakar, Yuming Feng*, Jinkui Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

For solving nonlinear monotone equations with convex constraints, Liu and Feng (Numer. Algoritm. 82(1):245–262, 2019) suggested a derivative-free iterative technique. Although they assert that the direction dk satisfies inequality (2.1), however, this is not true, as the derivation of the parameter θk given by equation (2.7) is not correct. This led to Lemma 2.2, Lemma 3.1 and Theorem 3.1 in Liu and Feng (Numer. Algoritm. 82(1):245–262, 2019) not holding. In addition, Theorem 3.1 is still invalid as the bound for ‖F(xk+αk′dk)‖ was not established by the authors, instead the authors used the bound for ‖ F(xk+ αkdk) ‖ as the bound for ‖F(xk+αk′dk)‖ . In this paper, We first describe the necessary adjustments and establish the bound for ‖F(xk+αk′dk)‖ , after which the proposed approach by Liu and Feng continues to converge globally. In addition, we provide some numerical results to support the adjustments.

Original languageEnglish
Pages (from-to)1551-1560
Number of pages10
JournalNumerical Algorithms
Volume94
Issue number4
DOIs
Publication statusPublished - Dec 2023
Externally publishedYes

Keywords

  • Global convergence
  • Linearly convergence rate
  • Monotone equations
  • Projection map

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