# Feedback control of Lagrange multipliers for non-smooth constrained optimization

arXiv: https://arxiv.org/abs/2604.06511 · HTML: https://mlsanity.com/paper/2604.06511/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2026.

## Built on by (most cited first, 1 of 1)

- [Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making](https://mlsanity.com/paper/2606.07088/) (2026)

## Abstract (arXiv)

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.