FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations

Auwal Bala Abubakar; Kanikar Muangchoo; Abdulkarim Hassan Ibrahim; Jamilu Abubakar; Sadiya Ali Rano

doi:10.1007/s40065-021-00313-5

FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations

Auwal Bala Abubakar, Kanikar Muangchoo^*, Abdulkarim Hassan Ibrahim, Jamilu Abubakar, Sadiya Ali Rano

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.

Original language	English
Pages (from-to)	261-270
Number of pages	10
Journal	Arabian Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/s40065-021-00313-5
Publication status	Published - Aug 2021
Externally published	Yes

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title = "FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations",

abstract = "This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.",

author = "Abubakar, {Auwal Bala} and Kanikar Muangchoo and Ibrahim, {Abdulkarim Hassan} and Jamilu Abubakar and Rano, {Sadiya Ali}",

note = "Funding Information: The first author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. The second author was financially supported by Rajamangala University of Technology Phra Nakhon (RMUTP) Research Scholarship. Funding Information: The first author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. The second author was financially supported by Rajamangala University of Technology Phra Nakhon (RMUTP) Research Scholarship. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

month = aug,

doi = "10.1007/s40065-021-00313-5",

language = "English",

volume = "10",

pages = "261--270",

journal = "Arabian Journal of Mathematics",

issn = "2193-5343",

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AU - Abubakar, Auwal Bala

AU - Muangchoo, Kanikar

AU - Ibrahim, Abdulkarim Hassan

AU - Abubakar, Jamilu

AU - Rano, Sadiya Ali

N1 - Funding Information: The first author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. The second author was financially supported by Rajamangala University of Technology Phra Nakhon (RMUTP) Research Scholarship. Funding Information: The first author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. The second author was financially supported by Rajamangala University of Technology Phra Nakhon (RMUTP) Research Scholarship. Publisher Copyright: © 2021, The Author(s).

PY - 2021/8

Y1 - 2021/8

N2 - This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.

AB - This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.

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DO - 10.1007/s40065-021-00313-5

M3 - Article

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VL - 10

SP - 261

EP - 270

JO - Arabian Journal of Mathematics

JF - Arabian Journal of Mathematics

SN - 2193-5343

IS - 2

ER -

FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations

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