Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917294500741120 |
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| author | Sun, Xiangkai He, Liang Long, Xianjun |
| author_facet | Sun, Xiangkai He, Liang Long, Xianjun |
| contents | This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of the primal-dual gap along the trajectory generated by the dynamical system, and provide some integral estimates. Then, based on the setting of the parameters involved, we demonstrate that both the convergence rate of the primal-dual gap and the strong convergence of the trajectory can be achieved simultaneously. Furthermore, we evaluate the performance of the proposed system using two numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problems Sun, Xiangkai He, Liang Long, Xianjun Optimization and Control 34D05(Primary) 37N40, 46N10, 90C25 (Secondary) This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of the primal-dual gap along the trajectory generated by the dynamical system, and provide some integral estimates. Then, based on the setting of the parameters involved, we demonstrate that both the convergence rate of the primal-dual gap and the strong convergence of the trajectory can be achieved simultaneously. Furthermore, we evaluate the performance of the proposed system using two numerical examples. |
| title | Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problems |
| topic | Optimization and Control 34D05(Primary) 37N40, 46N10, 90C25 (Secondary) |
| url | https://arxiv.org/abs/2412.05931 |