Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method
This study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and des...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-01-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2025.1477774/full |
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| author | Ghulam Abbass Nek Muhammad Katbar Israr Ahmed Memon Haibo Chen Fikadu Tesgera Tolasa Gemeda Tolessa Lubo |
| author_facet | Ghulam Abbass Nek Muhammad Katbar Israr Ahmed Memon Haibo Chen Fikadu Tesgera Tolasa Gemeda Tolessa Lubo |
| author_sort | Ghulam Abbass |
| collection | DOAJ |
| description | This study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and descent condition supported by carefully considered assumptions. The efficiency and effectiveness of the proposed method is highlighted by its outstanding numerical performance. To validate our claims, large-scale numerical simulations were conducted. These tests were designed to evaluate the capabilities of our proposed algorithm rigorously. In addition, we performed a comprehensive comparative numerical analysis, benchmarking our method against existing techniques. This analysis revealed that our approach consistently outperformed others in terms of theoretical robustness and numerical efficiency. The superiority of our method is evident in its ability to solve large-scale problems with accuracy in function evaluations, fewer iterations, and improved computational performance thereby, making it a valuable contribution to the field of numerical optimization. |
| format | Article |
| id | doaj-art-e5a0ed95e39c4cf2abf0b67e69a5bb15 |
| institution | Kabale University |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-e5a0ed95e39c4cf2abf0b67e69a5bb152025-01-29T06:46:14ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-01-011110.3389/fams.2025.14777741477774Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient methodGhulam Abbass0Nek Muhammad Katbar1Israr Ahmed Memon2Haibo Chen3Fikadu Tesgera Tolasa4Gemeda Tolessa Lubo5School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan, ChinaSchool of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan, ChinaDepartment of Mathematics, Shah Abdul Latif University, Khairpur, PakistanSchool of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan, ChinaDepartment of Mathematics, Dambi Dolla University, Dambi Dollo, EthiopiaDepartment of Mathematics, Dambi Dolla University, Dambi Dollo, EthiopiaThis study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the resolution of complex nonlinear problems. This innovative technique ensures global convergence and descent condition supported by carefully considered assumptions. The efficiency and effectiveness of the proposed method is highlighted by its outstanding numerical performance. To validate our claims, large-scale numerical simulations were conducted. These tests were designed to evaluate the capabilities of our proposed algorithm rigorously. In addition, we performed a comprehensive comparative numerical analysis, benchmarking our method against existing techniques. This analysis revealed that our approach consistently outperformed others in terms of theoretical robustness and numerical efficiency. The superiority of our method is evident in its ability to solve large-scale problems with accuracy in function evaluations, fewer iterations, and improved computational performance thereby, making it a valuable contribution to the field of numerical optimization.https://www.frontiersin.org/articles/10.3389/fams.2025.1477774/fullnon-linear equationconvex constraintsmonotone operatorglobal convergencespectral parameter |
| spellingShingle | Ghulam Abbass Nek Muhammad Katbar Israr Ahmed Memon Haibo Chen Fikadu Tesgera Tolasa Gemeda Tolessa Lubo Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method Frontiers in Applied Mathematics and Statistics non-linear equation convex constraints monotone operator global convergence spectral parameter |
| title | Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method |
| title_full | Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method |
| title_fullStr | Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method |
| title_full_unstemmed | Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method |
| title_short | Numerical optimization of large-scale monotone equations using the free-derivative spectral conjugate gradient method |
| title_sort | numerical optimization of large scale monotone equations using the free derivative spectral conjugate gradient method |
| topic | non-linear equation convex constraints monotone operator global convergence spectral parameter |
| url | https://www.frontiersin.org/articles/10.3389/fams.2025.1477774/full |
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