Accelerated derivative-free method for nonlinear monotone equations with an application

Abdulkarim Hassan Ibrahim, Poom Kumam*, Auwal Bala Abubakar, Abubakar Adamu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three-term derivative-free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133-145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.

Original languageEnglish
Article numbere2424
JournalNumerical Linear Algebra with Applications
Issue number3
Publication statusPublished - May 2022
Externally publishedYes


  • derivative-free method
  • inertial algorithm
  • iterative method
  • nonlinear equations
  • projection method


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