A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications
Abstract To address the challenges in engineering, social sciences, and large-scale limitations of traditional methods, this paper modifies a nonnegative conjugate coefficient to construct a search direction. This search direction has the sufficient descent property and trust-region feature without...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02087-7 |
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| _version_ | 1849710851301310464 |
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| author | Yan Xia Dandan Li Songhua Wang |
| author_facet | Yan Xia Dandan Li Songhua Wang |
| author_sort | Yan Xia |
| collection | DOAJ |
| description | Abstract To address the challenges in engineering, social sciences, and large-scale limitations of traditional methods, this paper modifies a nonnegative conjugate coefficient to construct a search direction. This search direction has the sufficient descent property and trust-region feature without relying on any line search approaches. By combining this with line search approaches and projection techniques, this paper proposes a modified two-term conjugate gradient-based algorithm, specifically for solving constrained nonlinear equations. The global convergence of the proposed algorithm is established without the need to require the Lipschitz continuity condition of nonlinear equations. Numerical experiments demonstrate that, compared to similar algorithms, the proposed algorithm is efficient and competitive in terms of the number of iterations, the number of function evaluations, and the running time. Additionally, it has been successfully applied to deal with image denoising problems. |
| format | Article |
| id | doaj-art-aefe8b0533dd4d0a95f4109e248b588e |
| institution | DOAJ |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-aefe8b0533dd4d0a95f4109e248b588e2025-08-20T03:14:46ZengSpringerOpenBoundary Value Problems1687-27702025-06-012025112210.1186/s13661-025-02087-7A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applicationsYan Xia0Dandan Li1Songhua Wang2School of Artificial Intelligence, Guangzhou Huashang CollegeSchool of Artificial Intelligence, Guangzhou Huashang CollegeSchool of Mathematics, Physics and Statistics, Baise UniversityAbstract To address the challenges in engineering, social sciences, and large-scale limitations of traditional methods, this paper modifies a nonnegative conjugate coefficient to construct a search direction. This search direction has the sufficient descent property and trust-region feature without relying on any line search approaches. By combining this with line search approaches and projection techniques, this paper proposes a modified two-term conjugate gradient-based algorithm, specifically for solving constrained nonlinear equations. The global convergence of the proposed algorithm is established without the need to require the Lipschitz continuity condition of nonlinear equations. Numerical experiments demonstrate that, compared to similar algorithms, the proposed algorithm is efficient and competitive in terms of the number of iterations, the number of function evaluations, and the running time. Additionally, it has been successfully applied to deal with image denoising problems.https://doi.org/10.1186/s13661-025-02087-7Two-term conjugate gradientProjection algorithmConstrained nonlinear equationsLarge-scaleImage denoising |
| spellingShingle | Yan Xia Dandan Li Songhua Wang A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications Boundary Value Problems Two-term conjugate gradient Projection algorithm Constrained nonlinear equations Large-scale Image denoising |
| title | A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications |
| title_full | A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications |
| title_fullStr | A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications |
| title_full_unstemmed | A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications |
| title_short | A modified two-term conjugate gradient-based projection algorithm for constrained nonlinear equations with applications |
| title_sort | modified two term conjugate gradient based projection algorithm for constrained nonlinear equations with applications |
| topic | Two-term conjugate gradient Projection algorithm Constrained nonlinear equations Large-scale Image denoising |
| url | https://doi.org/10.1186/s13661-025-02087-7 |
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