In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a plant whose equilibria correspond to the stationary points of the optimization problem. Within this framework, we propose two control strategies - a static controller and a dynamic controller - leading to two novel optimization algorithms. We provide a theoretical analysis, establishing global exponential convergence under strong convexity assumptions. Finally, we demonstrate the effectiveness of the proposed methods through numerical experiments, benchmarking their performance against state-of-the-art approaches.
@article{arxiv.2604.06511,
title = {Feedback control of Lagrange multipliers for non-smooth constrained optimization},
author = {V. Cerone and S. M. Fosson and S. Pirrera and A. Re and D. Regruto},
journal= {arXiv preprint arXiv:2604.06511},
year = {2026}
}