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

Abdulkarim Hassan Ibrahim; Poom Kumam; Auwal Bala Abubakar; Umar Batsari Yusuf; Seifu Endris Yimer; Kazeem Olalekan Aremu

doi:10.3934/math.2021016

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

Abdulkarim Hassan Ibrahim, Poom Kumam^*, Auwal Bala Abubakar, Umar Batsari Yusuf, Seifu Endris Yimer, Kazeem Olalekan Aremu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	235-260
Number of pages	26
Journal	AIMS Mathematics
Volume	6
Issue number	1
DOIs	https://doi.org/10.3934/math.2021016
State	Published - 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 the Author(s), licensee AIMS Press.

Keywords

Compressive sensing
Conjugate gradient method
Convex constrained
Nonlinear equations
Projection method
Unconstrained optimization

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2021016

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title = "An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration",

abstract = "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.",

keywords = "Compressive sensing, Conjugate gradient method, Convex constrained, Nonlinear equations, Projection method, Unconstrained optimization",

author = "Ibrahim, \{Abdulkarim Hassan\} and Poom Kumam and Abubakar, \{Auwal Bala\} and Yusuf, \{Umar Batsari\} and Yimer, \{Seifu Endris\} and Aremu, \{Kazeem Olalekan\}",

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doi = "10.3934/math.2021016",

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AU - Ibrahim, Abdulkarim Hassan

AU - Kumam, Poom

AU - Abubakar, Auwal Bala

AU - Yusuf, Umar Batsari

AU - Yimer, Seifu Endris

AU - Aremu, Kazeem Olalekan

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Compressive sensing

KW - Conjugate gradient method

KW - Convex constrained

KW - Nonlinear equations

KW - Projection method

KW - Unconstrained optimization

UR - https://www.scopus.com/pages/publications/85092552508

U2 - 10.3934/math.2021016

DO - 10.3934/math.2021016

M3 - Article

AN - SCOPUS:85092552508

SN - 2473-6988

VL - 6

SP - 235

EP - 260

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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