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

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

Other (Strategic Research Themes)

Publication Details

Author list: Ibrahim, Abdulkarim Hassan; Kumam, Poom; Abubakar, Auwal Bala; Abubakar, Jamilu;

Publisher: Wiley

Publication year: 2023

Journal: Mathematical Methods in the Applied Sciences (0170-4214)

Volume number: 46

Issue number: 8

ISSN: 0170-4214

eISSN: 1099-1476

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85147223274&doi=10.1002%2fmma.9033&partnerID=40&md5=74a566e2cb41a51a73b049f1035c5f74

Languages: English-Great Britain (EN-GB)

View in Web of Science | View on publisher site | View citing articles in Web of Science

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. © 2023 John Wiley & Sons, Ltd.

Keywords

No matching items found.