Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917771573460992 |
|---|---|
| author | Sun, Xiangkai He, Liang Long, Xian-Jun |
| author_facet | Sun, Xiangkai He, Liang Long, Xian-Jun |
| contents | In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing speed of the rescaled regularization parameter (i.e., the product of Tikhonov regularization parameter and general time scaling parameter), we analyze the convergence properties of the trajectory generated by the dynamical system. When the rescaled regularization parameter decreases rapidly to zero, we obtain convergence rates of the primal-dual gap and velocity vector along the trajectory generated by the dynamical system. In the case that the rescaled regularization parameter tends slowly to zero, we show the strong convergence of the trajectory towards the minimal norm solution of the convex-concave bilinear saddle point problem. Further, we also present some numerical experiments to illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems Sun, Xiangkai He, Liang Long, Xian-Jun Optimization and Control 34D05, 37N40, 46N10, 90C25 In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing speed of the rescaled regularization parameter (i.e., the product of Tikhonov regularization parameter and general time scaling parameter), we analyze the convergence properties of the trajectory generated by the dynamical system. When the rescaled regularization parameter decreases rapidly to zero, we obtain convergence rates of the primal-dual gap and velocity vector along the trajectory generated by the dynamical system. In the case that the rescaled regularization parameter tends slowly to zero, we show the strong convergence of the trajectory towards the minimal norm solution of the convex-concave bilinear saddle point problem. Further, we also present some numerical experiments to illustrate the theoretical results. |
| title | Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems |
| topic | Optimization and Control 34D05, 37N40, 46N10, 90C25 |
| url | https://arxiv.org/abs/2409.05301 |