# A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimization

arXiv: https://arxiv.org/abs/1902.03319 · HTML: https://mlsanity.com/paper/1902.03319/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Revisiting Implicit Differentiation for Learning Problems in Optimal Control](https://mlsanity.com/paper/2310.14468/) (2023)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learning](https://mlsanity.com/paper/2402.05421/) (2024)
- [DiffCoord: Differentiable Coordination for Distributed Multi-Agent Trajectory Optimization](https://mlsanity.com/paper/2509.01630/) (2025)

## Abstract (arXiv)

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose nonlinear optimization solver that is well suited to bilevel optimization. We then demonstrate the validity and scalability of our algorithm with two representative robotic problems, namely robust control and parameter estimation for a system involving contact. We stress the general nature of the algorithm and its potential relevance to many other problems in robotics.