PROJECTION METHOD WITH INERTIAL STEP FOR NONLINEAR EQUATIONS: APPLICATION TO SIGNAL RECOVERY

Abdulkarim Hassan Ibrahim*, Poom Kumam, Min Sun, Parin Chaipunya, Auwal Bala Abubakar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

In this paper, using the concept of inertial extrapolation, we introduce a globally convergent inertial extrapolation method for solving nonlinear equations with convex constraints for which the underlying mapping is monotone and Lipschitz continuous. The method can be viewed as a combination of the efficient three-term derivative-free method of Gao and He [Calcolo. 55(4), 1-17, 2018] with the inertial extrapolation step. Moreover, the algorithm is designed such that at every iteration, the method is free from derivative evaluations. Under standard assumptions, we establish the global convergence results for the proposed method. Numerical implementations illustrate the performance and advantage of this new method. Moreover, we also extend this method to solve the LASSO problems to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of our algorithm.

Original languageEnglish
Pages (from-to)30-55
Number of pages26
JournalJournal of Industrial and Management Optimization
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 2023
Externally publishedYes

Keywords

  • Derivativefree method
  • Inertial algorithm
  • Iterative method
  • Nonlinear equations
  • Projection method
  • Signal recovery.

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