Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917396833370112 |
|---|---|
| author | Centorrino, Veronica Rossi, Francesca Bullo, Francesco Russo, Giovanni |
| author_facet | Centorrino, Veronica Rossi, Francesca Bullo, Francesco Russo, Giovanni |
| contents | This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these optimization problems, inspired by recent results, we introduce the \emph{proportional--integral proximal gradient dynamics} (PI--PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the stationary points of the minimization problem and the equilibria of the PI--PGD. Then for the case of affine constraints, by leveraging tools from contraction theory we give a comprehensive convergence analysis for the dynamics, showing linear--exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an exploratory application to nonlinear equality constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization Centorrino, Veronica Rossi, Francesca Bullo, Francesco Russo, Giovanni Optimization and Control Systems and Control This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these optimization problems, inspired by recent results, we introduce the \emph{proportional--integral proximal gradient dynamics} (PI--PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the stationary points of the minimization problem and the equilibria of the PI--PGD. Then for the case of affine constraints, by leveraging tools from contraction theory we give a comprehensive convergence analysis for the dynamics, showing linear--exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an exploratory application to nonlinear equality constraints. |
| title | Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2503.15093 |