An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the g...

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Bibliographic Details
Published in:AIMS mathematics Vol. 6; no. 1; pp. 235 - 260
Main Authors: Ibrahim, Abdulkarim Hassan, Kumam, Poom, Abubakar, Auwal Bala, Yusuf, Umar Batsari, Yimer, Seifu Endris, Aremu, Kazeem Olalekan
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2021
Subjects:
compressive sensing
conjugate gradient method
convex constrained
nonlinear equations
projection method
unconstrained optimization
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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Summary:Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021016