An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications
This research paper proposes a derivative-free method for solving systems of nonlinear<br />equations with closed and convex constraints, where the functions under consideration are continuous<br />and monotone. Given an initial iterate, the process first generates a specific direction a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/9/767 |
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| author | Auwal Bala Abubakar Poom Kumam Hassan Mohammad Aliyu Muhammed Awwal |
| author_facet | Auwal Bala Abubakar Poom Kumam Hassan Mohammad Aliyu Muhammed Awwal |
| author_sort | Auwal Bala Abubakar |
| collection | DOAJ |
| description | This research paper proposes a derivative-free method for solving systems of nonlinear<br />equations with closed and convex constraints, where the functions under consideration are continuous<br />and monotone. Given an initial iterate, the process first generates a specific direction and then employs<br />a line search strategy along the direction to calculate a new iterate. If the new iterate solves the<br />problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set<br />(constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent<br />condition and the global convergence of the method is established under suitable assumptions.<br />Finally, some numerical experiments were presented to show the performance of the proposed<br />method in solving nonlinear equations and its application in image recovery problems. |
| first_indexed | 2024-12-21T12:53:39Z |
| format | Article |
| id | doaj.art-11b9cf1b4b9341dca3ab9cdac1ddbff9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T12:53:39Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-11b9cf1b4b9341dca3ab9cdac1ddbff92022-12-21T19:03:25ZengMDPI AGMathematics2227-73902019-08-017976710.3390/math7090767math7090767An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with ApplicationsAuwal Bala Abubakar0Poom Kumam1Hassan Mohammad2Aliyu Muhammed Awwal3KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandKMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandDepartment of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano 700241, NigeriaKMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandThis research paper proposes a derivative-free method for solving systems of nonlinear<br />equations with closed and convex constraints, where the functions under consideration are continuous<br />and monotone. Given an initial iterate, the process first generates a specific direction and then employs<br />a line search strategy along the direction to calculate a new iterate. If the new iterate solves the<br />problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set<br />(constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent<br />condition and the global convergence of the method is established under suitable assumptions.<br />Finally, some numerical experiments were presented to show the performance of the proposed<br />method in solving nonlinear equations and its application in image recovery problems.https://www.mdpi.com/2227-7390/7/9/767nonlinear monotone equationsconjugate gradient methodprojection methodsignal processing |
| spellingShingle | Auwal Bala Abubakar Poom Kumam Hassan Mohammad Aliyu Muhammed Awwal An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications Mathematics nonlinear monotone equations conjugate gradient method projection method signal processing |
| title | An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications |
| title_full | An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications |
| title_fullStr | An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications |
| title_full_unstemmed | An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications |
| title_short | An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications |
| title_sort | efficient conjugate gradient method for convex constrained monotone nonlinear equations with applications |
| topic | nonlinear monotone equations conjugate gradient method projection method signal processing |
| url | https://www.mdpi.com/2227-7390/7/9/767 |
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