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

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]...

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Bibliographic Details
Published in:Numerical linear algebra with applications Vol. 29; no. 3
Main Authors: Hassan Ibrahim, Abdulkarim, Kumam, Poom, Bala Abubakar, Auwal, Adamu, Abubakar
Format: Journal Article
Language:English
Published: Oxford Wiley Subscription Services, Inc 01.05.2022
Subjects:
Algorithms
Convergence
derivative‐free method
inertial algorithm
iterative method
Iterative methods
Nonlinear equations
Operators (mathematics)
Optimization
Performance assessment
projection method
ISSN:1070-5325, 1099-1506
Online Access:Get full text
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Summary: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.
Bibliography:Funding information
Center of Excellence in Theoretical and Computational Science (TaCS‐CoE), KMUTT, King Mongkut's University of Technology Thonburi, National Council of Thailand (NRCT)
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2424