Primal-dual dynamical systems with closed-loop control for convex optimization in continuous and discrete time
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911474336661504 |
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| author | Zhang, Huan Sun, Xiangkai Li, Shengjie Teo, Kok Lay |
| author_facet | Zhang, Huan Sun, Xiangkai Li, Shengjie Teo, Kok Lay |
| contents | This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" + ``first-order dual'' continuous-time dynamical system, in which both the time scaling and Hessian-driven damping are governed by a feedback control of the gradient for the Lagrangian function. This system achieves the fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along its trajectory. Subsequently, by time discretization of this system, we develop an accelerated primal-dual algorithm with a gradient-defined adaptive step size. We also obtain convergence rates for the primal-dual gap, the feasibility violation, and the objective residual. Furthermore, we provide numerical results to demonstrate the practical efficacy and superior performance of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Primal-dual dynamical systems with closed-loop control for convex optimization in continuous and discrete time Zhang, Huan Sun, Xiangkai Li, Shengjie Teo, Kok Lay Optimization and Control 34D05, 37N40, 90C25 This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" + ``first-order dual'' continuous-time dynamical system, in which both the time scaling and Hessian-driven damping are governed by a feedback control of the gradient for the Lagrangian function. This system achieves the fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along its trajectory. Subsequently, by time discretization of this system, we develop an accelerated primal-dual algorithm with a gradient-defined adaptive step size. We also obtain convergence rates for the primal-dual gap, the feasibility violation, and the objective residual. Furthermore, we provide numerical results to demonstrate the practical efficacy and superior performance of the proposed algorithm. |
| title | Primal-dual dynamical systems with closed-loop control for convex optimization in continuous and discrete time |
| topic | Optimization and Control 34D05, 37N40, 90C25 |
| url | https://arxiv.org/abs/2602.16402 |