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

Author:

Ibrahim Abdulkarim Hassan12ORCID,Kumam Poom13ORCID,Abubakar Auwal Bala24ORCID,Abubakar Jamilu5ORCID

Affiliation:

1. Center of Excellence in Theoretical and Computational Science (TaCS‐CoE), 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thung Khru Bangkok 10140 Thailand

2. Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Ga‐Rankuwa Pretoria 0204 Medunsa South Africa

3. Department of Medical Research China Medical University Hospital, China Medical University Taichung 40402 Taiwan

4. Department of Mathematical Sciences, Faculty of Physical Sciences Bayero University, Kano Kano Nigeria

5. Department of Mathematics Usmanu Danfodiyo University Sokoto Nigeria

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.

Publisher

Wiley

Subject

General Engineering,General Mathematics

Reference48 articles.

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