A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration
This paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed algorithm presents several significant advancements and key features: (i) the conjugate parameter is constructed by utilizing the hybrid technique; (i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241717 |
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| _version_ | 1832590721657339904 |
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| author | Xuejie Ma Songhua Wang |
| author_facet | Xuejie Ma Songhua Wang |
| author_sort | Xuejie Ma |
| collection | DOAJ |
| description | This paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed algorithm presents several significant advancements and key features: (i) the conjugate parameter is constructed by utilizing the hybrid technique; (ii) the search direction, designed with the conjugate parameter, possesses sufficient descent and trust region properties without the need for a line search mechanism; (iii) the global convergence is rigorously established under general assumptions, notably without the requirement of the Lipschitz continuity condition; (vi) numerical experiments demonstrate the algorithm's efficiency, particularly in solving large-scale constrained nonlinear systems of equations and addressing the sparse signal restoration problem. |
| format | Article |
| id | doaj-art-05a243c59b9a48bd9a707fe8f2903961 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-05a243c59b9a48bd9a707fe8f29039612025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912361673619010.3934/math.20241717A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restorationXuejie Ma0Songhua Wang1School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou 511300, ChinaSchool of Mathematics, Physics and Statistics, Baise University, Baise 533099, ChinaThis paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed algorithm presents several significant advancements and key features: (i) the conjugate parameter is constructed by utilizing the hybrid technique; (ii) the search direction, designed with the conjugate parameter, possesses sufficient descent and trust region properties without the need for a line search mechanism; (iii) the global convergence is rigorously established under general assumptions, notably without the requirement of the Lipschitz continuity condition; (vi) numerical experiments demonstrate the algorithm's efficiency, particularly in solving large-scale constrained nonlinear systems of equations and addressing the sparse signal restoration problem.https://www.aimspress.com/article/doi/10.3934/math.20241717constrained nonlinear systems of equationsconjugate gradient methodlarge-scaleglobal convergencesignal reconstruction |
| spellingShingle | Xuejie Ma Songhua Wang A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration AIMS Mathematics constrained nonlinear systems of equations conjugate gradient method large-scale global convergence signal reconstruction |
| title | A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| title_full | A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| title_fullStr | A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| title_full_unstemmed | A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| title_short | A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| title_sort | hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration |
| topic | constrained nonlinear systems of equations conjugate gradient method large-scale global convergence signal reconstruction |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241717 |
| work_keys_str_mv | AT xuejiema ahybridapproachtoconjugategradientalgorithmsfornonlinearsystemsofequationswithapplicationsinsignalrestoration AT songhuawang ahybridapproachtoconjugategradientalgorithmsfornonlinearsystemsofequationswithapplicationsinsignalrestoration AT xuejiema hybridapproachtoconjugategradientalgorithmsfornonlinearsystemsofequationswithapplicationsinsignalrestoration AT songhuawang hybridapproachtoconjugategradientalgorithmsfornonlinearsystemsofequationswithapplicationsinsignalrestoration |