A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications
In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction...
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| Veröffentlicht in: | Numerical algorithms Jg. 88; H. 1; S. 389 - 418 |
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| Format: | Journal Article |
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01.09.2021
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| ISSN: | 1017-1398, 1572-9265 |
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| Abstract | In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction generated by the proposed method is close to the one yielded by the memoryless BFGS method, and has the sufficient descent property and the trust region property independent of line search technique. Under some mild conditions, we establish the global convergence of the proposed method. Our numerical experiments show the effectiveness and robustness of the proposed method in comparison with two existing algorithms in the literature. Moreover, we show applicability and encouraging efficiency of the proposed method by extending it to solve sparse signal restoration and image de-blurring problems. |
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| AbstractList | In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction generated by the proposed method is close to the one yielded by the memoryless BFGS method, and has the sufficient descent property and the trust region property independent of line search technique. Under some mild conditions, we establish the global convergence of the proposed method. Our numerical experiments show the effectiveness and robustness of the proposed method in comparison with two existing algorithms in the literature. Moreover, we show applicability and encouraging efficiency of the proposed method by extending it to solve sparse signal restoration and image de-blurring problems. |
| Author | Wang, Lingzhi Liu, Meixing Yin, Jianghua Jian, Jinbao Jiang, Xianzhen |
| Author_xml | – sequence: 1 givenname: Jianghua surname: Yin fullname: Yin, Jianghua organization: School of Mathematical Sciences, Inner Mongolia University – sequence: 2 givenname: Jinbao orcidid: 0000-0001-8048-7397 surname: Jian fullname: Jian, Jinbao email: jianjb@gxu.edu.cn organization: College of Mathematics and Physics, Guangxi University for Nationalities – sequence: 3 givenname: Xianzhen surname: Jiang fullname: Jiang, Xianzhen organization: College of Mathematics and Physics, Guangxi University for Nationalities – sequence: 4 givenname: Meixing surname: Liu fullname: Liu, Meixing organization: Department of Mathematics, Shanghai University – sequence: 5 givenname: Lingzhi surname: Wang fullname: Wang, Lingzhi organization: School of Mechanical and Electrical Engineering, Guangxi Science and Technology Normal University |
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| Keywords | Three-term conjugate gradient method 68U10 65K10 Convergence property Compressed sensing Derivative-free projection method |
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| SubjectTerms | Adaptive search techniques Algebra Algorithms Blurring Computer Science Conjugate gradient method Constraints Mathematical analysis Methods Numeric Computing Numerical Analysis Optimization Original Paper Robustness (mathematics) Searching Theory of Computation |
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| Title | A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications |
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