Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization

[2503.15093] Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2503.15093 (math) [Submitted on 19 Mar 2025 ( v1 ), last revised 19 Jun 2026 (this version, v5)] Title: Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization Authors: Veronica Centorrino , Francesca Rossi , Francesco Bullo , Giovanni Russo View a PDF of the paper titled Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization, by Veronica Centorrino and Francesca Rossi and Francesco Bullo and Giovanni Russo View PDF HTML (experimental) Abstract: 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 convergence to a stationary point. Moreover, under suitable assumptions, we show 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. Comments: 19 pages, 13 figures Subjects: Optimization and Control (math.OC) ; Systems and Control (eess.SY) Cite as: arXiv:2503.15093 [math.OC] (or arXiv:2503.15093v5 [math.OC] for this version) https://doi.org/10.48550/arXiv.2503.15093 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Veronica Centorrino [ view email ] [v1] Wed, 19 Mar 2025 10:47:16 UTC (1,671 KB) [v2] Wed, 7 May 2025 22:47:29 UTC (2,843 KB) [v3] Wed, 5 Nov 2025 14:18:57 UTC (2,577 KB) [v4] Fri, 10 Apr 2026 12:26:14 UTC (2,571 KB) [v5] Fri, 19 Jun 2026 18:43:08 UTC (6,741 KB) Full-text links: Access Paper: View a PDF of the paper titled Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization, by Veronica Centorrino and Francesca Rossi and Francesco Bullo and Giovanni Russo View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-03 Change to browse by: cs cs.SY eess eess.SY math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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