# On the Generalised Langevin Equation for Simulated Annealing

arXiv: https://arxiv.org/abs/2003.06448 · HTML: https://mlsanity.com/paper/2003.06448/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2020.

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

- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [Equality Constrained Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2410.01939/) (2024)
- [Provable Accuracy Bounds for Hybrid Dynamical Optimization and Sampling](https://mlsanity.com/paper/2410.06397/) (2024)

## Abstract (arXiv)

In this paper, we consider the generalised (higher order) Langevin equation for the purpose of simulated annealing and optimisation of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian noise with an appropriate Ornstein-Uhlenbeck process to account for memory in the system. Under reasonable conditions on the loss function and the annealing schedule, we establish convergence of the continuous time dynamics to a global minimum. In addition, we investigate the performance numerically and show better performance and higher exploration of the state space compared to the underdamped and overdamped Langevin dynamics with the same annealing schedule.