Symplectic Extra-gradient Type Method for Solving General Non-monotone Inclusion Problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908276357070848 |
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| author | Yuan, Ya-xiang Zhang, Yi |
| author_facet | Yuan, Ya-xiang Zhang, Yi |
| contents | In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of the initial point, which can potentially decelerate numerical convergence rate. In this work, we present a new accelerated extra-gradient method, by utilizing the symplectic acceleration technique. We establish the inverse of quadratic convergence rate by employing the Lyapunov function technique. Also, we demonstrate a faster inverse of quadratic convergence rate alongside its weak convergence property under stronger assumptions. To improve practical efficiency, we introduce a line search technique for our symplectic extra-gradient method. Theoretically, we prove the convergence of the symplectic extra-gradient method with line search. Numerical tests show that this adaptation exhibits faster convergence rates in practice compared to several existing extra-gradient type methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_10793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic Extra-gradient Type Method for Solving General Non-monotone Inclusion Problem Yuan, Ya-xiang Zhang, Yi Optimization and Control 47J20, 47H05, 65K10, 65K15, 65Y20, 90C30, 90C52 In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of the initial point, which can potentially decelerate numerical convergence rate. In this work, we present a new accelerated extra-gradient method, by utilizing the symplectic acceleration technique. We establish the inverse of quadratic convergence rate by employing the Lyapunov function technique. Also, we demonstrate a faster inverse of quadratic convergence rate alongside its weak convergence property under stronger assumptions. To improve practical efficiency, we introduce a line search technique for our symplectic extra-gradient method. Theoretically, we prove the convergence of the symplectic extra-gradient method with line search. Numerical tests show that this adaptation exhibits faster convergence rates in practice compared to several existing extra-gradient type methods. |
| title | Symplectic Extra-gradient Type Method for Solving General Non-monotone Inclusion Problem |
| topic | Optimization and Control 47J20, 47H05, 65K10, 65K15, 65Y20, 90C30, 90C52 |
| url | https://arxiv.org/abs/2406.10793 |