A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

Abdulkarim Hassan Ibrahim; Poom Kumam; Basim A. Hassan; Auwal Bala Abubakar; Jamilu Abubakar

doi:10.1080/00207160.2021.1946043

A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

Abdulkarim Hassan Ibrahim, Poom Kumam^*, Basim A. Hassan, Auwal Bala Abubakar, Jamilu Abubakar

^*Corresponding author for this work

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

19 Scopus citations

Abstract

In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

Original language	English
Pages (from-to)	1041-1065
Number of pages	25
Journal	International Journal of Computer Mathematics
Volume	99
Issue number	5
DOIs	https://doi.org/10.1080/00207160.2021.1946043
State	Published - 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

65K05
65L09
90C30
Unconstrained optimization
compressive sensing
conjugate gradient method
derivative-free method
nonlinear equations
projection method

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.1080/00207160.2021.1946043

Cite this

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title = "A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration",

abstract = "In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.",

keywords = "65K05, 65L09, 90C30, Unconstrained optimization, compressive sensing, conjugate gradient method, derivative-free method, nonlinear equations, projection method",

author = "\{Hassan Ibrahim\}, Abdulkarim and Poom Kumam and Hassan, \{Basim A.\} and \{Bala Abubakar\}, Auwal and Jamilu Abubakar",

note = "Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2022",

doi = "10.1080/00207160.2021.1946043",

language = "English",

volume = "99",

pages = "1041--1065",

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T1 - A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

AU - Hassan Ibrahim, Abdulkarim

AU - Kumam, Poom

AU - Hassan, Basim A.

AU - Bala Abubakar, Auwal

AU - Abubakar, Jamilu

PY - 2022

Y1 - 2022

N2 - In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

AB - In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

KW - 65K05

KW - 65L09

KW - 90C30

KW - Unconstrained optimization

KW - compressive sensing

KW - conjugate gradient method

KW - derivative-free method

KW - nonlinear equations

KW - projection method

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U2 - 10.1080/00207160.2021.1946043

DO - 10.1080/00207160.2021.1946043

M3 - Article

AN - SCOPUS:85109780938

SN - 0020-7160

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SP - 1041

EP - 1065

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

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ER -

A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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