A derivative-free projection method for nonlinear equations with non-Lipschitz operator: Application to LASSO problem

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we introduce a derivative-free iterative method for finding the solutions of convex constrained nonlinear equations (CCNE) using the projection strategy. The new approach is free from gradient evaluations at each iteration. Also, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Compared with traditional methods for solving CCNE that assumes Lipschitz continuity and monotonicity to establish the global convergence result, an advantage of our proposed method is that the global convergence result does not require the assumption of Lipschitz continuity. Moreover, the underlying operator is assumed to be pseudomonotone, which is a milder condition than monotonicity. As an applications, we solve the LASSO problem in compressed sensing. Numerical experiments illustrate the performances of our proposed algorithm and provide a comparison with related algorithms.

Original languageEnglish
JournalMathematical Methods in the Applied Sciences
DOIs
Publication statusAccepted/In press - 2023
Externally publishedYes

Keywords

  • derivative-free method
  • iterative method
  • nonlinear equations
  • projection method
  • pseudomonotone operator

Fingerprint

Dive into the research topics of 'A derivative-free projection method for nonlinear equations with non-Lipschitz operator: Application to LASSO problem'. Together they form a unique fingerprint.

Cite this