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Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations

Predrag S. Stanimirović Orcid Logo, Bilall I. Shaini, Jamilu Sabi’u, Abdullah Shah, Milena J. Petrović Orcid Logo, Branislav Ivanov Orcid Logo, Xinwei Cao, Alena Stupina, Shuai Li Orcid Logo

Algorithms, Volume: 16, Issue: 2, Start page: 64

Swansea University Author: Shuai Li Orcid Logo

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DOI (Published version): 10.3390/a16020064

Abstract

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated doub...

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Published in: Algorithms
ISSN: 1999-4893
Published: MDPI AG 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62798
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spelling 2023-04-20T16:42:03.7408644 v2 62798 2023-03-06 Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations 42ff9eed09bcd109fbbe484a0f99a8a8 0000-0001-8316-5289 Shuai Li Shuai Li true false 2023-03-06 ACEM This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE. Journal Article Algorithms 16 2 64 MDPI AG 1999-4893 18 1 2023 2023-01-18 10.3390/a16020064 http://dx.doi.org/10.3390/a16020064 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Predrag Stanimirović is supported by the Science Fund of the Republic of Serbia, (No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications-QUAM). Predrag Stanimirović acknowledges support Grant No. 451-03-68/2022-14/200124 given by Ministry of Education, Science and Technological Development, Republic of Serbia. Milena J. Petrović acknowledges support Grant No.174025 given by Ministry of Education, Science and Technological Development, Republic of Serbia. Milena J. Petrović acknowledges support from the internal-junior project IJ-0202 given by the Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, Serbia. 2023-04-20T16:42:03.7408644 2023-03-06T11:22:57.5073176 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Predrag S. Stanimirović 0000-0003-0655-3741 1 Bilall I. Shaini 2 Jamilu Sabi’u 3 Abdullah Shah 4 Milena J. Petrović 0000-0002-5073-143x 5 Branislav Ivanov 0000-0001-9179-0965 6 Xinwei Cao 7 Alena Stupina 8 Shuai Li 0000-0001-8316-5289 9 62798__26750__2886815b0d274ce3a4afaa7f1fd7c475.pdf 62798.pdf 2023-03-06T11:26:49.1050624 Output 843232 application/pdf Version of Record true This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). true eng https://creativecommons.org/licenses/by/4.0/
title Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
spellingShingle Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
Shuai Li
title_short Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
title_full Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
title_fullStr Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
title_full_unstemmed Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
title_sort Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
author_id_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8
author_id_fullname_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8_***_Shuai Li
author Shuai Li
author2 Predrag S. Stanimirović
Bilall I. Shaini
Jamilu Sabi’u
Abdullah Shah
Milena J. Petrović
Branislav Ivanov
Xinwei Cao
Alena Stupina
Shuai Li
format Journal article
container_title Algorithms
container_volume 16
container_issue 2
container_start_page 64
publishDate 2023
institution Swansea University
issn 1999-4893
doi_str_mv 10.3390/a16020064
publisher MDPI AG
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
url http://dx.doi.org/10.3390/a16020064
document_store_str 1
active_str 0
description This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.
published_date 2023-01-18T06:25:24Z
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