# Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

arXiv: https://arxiv.org/abs/1611.02023 · HTML: https://mlsanity.com/paper/1611.02023/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2016.

## Built on by (most cited first, 6 of 6)

- [Policy Gradient for Continuous-Time Mean-Field Control](https://mlsanity.com/paper/2605.20718/) (2026)
- [Exploration noise for learning linear-quadratic mean field games](https://mlsanity.com/paper/2107.00839/) (2021)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data](https://mlsanity.com/paper/2606.26498/) (2026)
- [Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type](https://mlsanity.com/paper/2210.00874/) (2022)

## Abstract (arXiv)

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditions are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.