# Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems

arXiv: https://arxiv.org/abs/2402.13988 · HTML: https://mlsanity.com/paper/2402.13988/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time](https://mlsanity.com/paper/2606.17260/) (2026)
- [Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo](https://mlsanity.com/paper/2607.12902/) (2026)

## Abstract (arXiv)

We propose an optimization algorithm called Frictionless Hamiltonian Descent, which is a direct counterpart of classical Hamiltonian Monte Carlo in sampling. We analyze Frictionless Hamiltonian Descent for strongly convex quadratic functions and show that the method has a non-trivial accelerated rate comparable to that of Heavy Ball flow. We also propose Frictionless Coordinate Hamiltonian Descent and its parallelizable variant, which together encompass the classical Gauss-Seidel method, Successive Over-relaxation, Jacobi method, and more, for solving a linear system of equations. The result not only offers a new perspective on these existing algorithms but also leads to a broader class of update schemes that guarantee convergence.