# Derivation of Coordinate Descent Algorithms from Optimal Control Theory

arXiv: https://arxiv.org/abs/2309.03990 · HTML: https://mlsanity.com/paper/2309.03990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 3 of 3)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)

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

- [On The Mathematics of the Natural Physics of Optimization](https://mlsanity.com/paper/2604.17645/) (2026)

## Abstract (arXiv)

Recently, it was posited that disparate optimization algorithms may be coalesced in terms of a central source emanating from optimal control theory. Here we further this proposition by showing how coordinate descent algorithms may be derived from this emerging new principle. In particular, we show that basic coordinate descent algorithms can be derived using a maximum principle and a collection of max functions as "control" Lyapunov functions. The convergence of the resulting coordinate descent algorithms is thus connected to the controlled dissipation of their corresponding Lyapunov functions. The operational metric for the search vector in all cases is given by the Hessian of the convex objective function.