# A closed loop gradient descent algorithm applied to Rosenbrock's function

arXiv: https://arxiv.org/abs/2108.12883 · HTML: https://mlsanity.com/paper/2108.12883/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 29 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [A Variational Perspective on Accelerated Methods in Optimization](https://mlsanity.com/paper/1603.04245/) (2016)
- [A Dynamical Systems Perspective on Nesterov Acceleration](https://mlsanity.com/paper/1905.07436/) (2019)
- [Continuous Time Analysis of Momentum Methods](https://mlsanity.com/paper/1906.04285/) (2019)
- [A general system of differential equations to model first order adaptive algorithms](https://mlsanity.com/paper/1810.13108/) (2018)
- [Fast optimization via inertial dynamics with closed-loop damping](https://mlsanity.com/paper/2008.02261/) (2020)

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

- [Whiplash Gradient Descent Dynamics](https://mlsanity.com/paper/2203.02140/) (2022)

## Abstract (arXiv)

We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an improvement on existing momentum-based gradient optimisation methods. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous-time version of the algorithm. Using numerical simulations, we consider the performance of its discrete-time counterpart obtained by using the symplectic Euler method of discretisation.