# A new framework for constrained optimization via feedback control of Lagrange multipliers

arXiv: https://arxiv.org/abs/2403.12738 · HTML: https://mlsanity.com/paper/2403.12738/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2024.

## Built on by (most cited first, 3 of 3)

- [A Control Perspective on Training PINNs](https://mlsanity.com/paper/2501.18582/) (2025)
- [AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training](https://mlsanity.com/paper/2605.08408/) (2026)
- [Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making](https://mlsanity.com/paper/2606.07088/) (2026)

## Abstract (arXiv)

The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a feedback control system where the Lagrange multipliers are the control input, and the output represents the constraints. The system converges to a stationary point of the constrained optimization problem through suitable regulation. Regarding the Lagrange multipliers, we consider two control laws: proportional-integral control and feedback linearization. These choices give rise to a family of different methods. We rigorously develop the related algorithms, theoretically analyze their convergence and present several numerical experiments to support their effectiveness concerning the state-of-the-art approaches.