Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery
This paper proposes a modified Rivaie-Mohd-Ismail-Leong (RMIL)-type conjugate gradient algorithm for solving nonlinear systems of equations with convex constraints. The proposed algorithm offers several key characteristics: (1) The modified conjugate parameter is non-negative, thereby enhancing the...
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024286 |
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| author | Yan Xia Songhua Wang |
| author_facet | Yan Xia Songhua Wang |
| author_sort | Yan Xia |
| collection | DOAJ |
| description | This paper proposes a modified Rivaie-Mohd-Ismail-Leong (RMIL)-type conjugate gradient algorithm for solving nonlinear systems of equations with convex constraints. The proposed algorithm offers several key characteristics: (1) The modified conjugate parameter is non-negative, thereby enhancing the proposed algorithm's stability. (2) The search direction satisfies sufficient descent and trust region properties without relying on any line search technique. (3) The global convergence of the proposed algorithm is established under general assumptions without requiring the Lipschitz continuity condition for nonlinear systems of equations. (4) Numerical experiments indicated that the proposed algorithm surpasses existing similar algorithms in both efficiency and stability, particularly when applied to large scale nonlinear systems of equations and signal recovery problems in compressed sensing. |
| format | Article |
| id | doaj-art-2855f7f46cd041f49d8fc4be48a825bf |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-2855f7f46cd041f49d8fc4be48a825bf2025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116153617410.3934/era.2024286Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recoveryYan Xia0Songhua Wang1School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou 511300, ChinaSchool of Mathematics, Physics and Statistics, Baise University, Baise 533099, ChinaThis paper proposes a modified Rivaie-Mohd-Ismail-Leong (RMIL)-type conjugate gradient algorithm for solving nonlinear systems of equations with convex constraints. The proposed algorithm offers several key characteristics: (1) The modified conjugate parameter is non-negative, thereby enhancing the proposed algorithm's stability. (2) The search direction satisfies sufficient descent and trust region properties without relying on any line search technique. (3) The global convergence of the proposed algorithm is established under general assumptions without requiring the Lipschitz continuity condition for nonlinear systems of equations. (4) Numerical experiments indicated that the proposed algorithm surpasses existing similar algorithms in both efficiency and stability, particularly when applied to large scale nonlinear systems of equations and signal recovery problems in compressed sensing.https://www.aimspress.com/article/doi/10.3934/era.2024286nonlinear systems of equationsconjugate gradient methodlarge scaleglobal convergencesignal recovery |
| spellingShingle | Yan Xia Songhua Wang Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery Electronic Research Archive nonlinear systems of equations conjugate gradient method large scale global convergence signal recovery |
| title | Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| title_full | Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| title_fullStr | Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| title_full_unstemmed | Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| title_short | Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| title_sort | global convergence in a modified rmil type conjugate gradient algorithm for nonlinear systems of equations and signal recovery |
| topic | nonlinear systems of equations conjugate gradient method large scale global convergence signal recovery |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024286 |
| work_keys_str_mv | AT yanxia globalconvergenceinamodifiedrmiltypeconjugategradientalgorithmfornonlinearsystemsofequationsandsignalrecovery AT songhuawang globalconvergenceinamodifiedrmiltypeconjugategradientalgorithmfornonlinearsystemsofequationsandsignalrecovery |