# Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time

arXiv: https://arxiv.org/abs/2606.17260 · HTML: https://mlsanity.com/paper/2606.17260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 6 of 6)

- [Gradient methods for convex minimization: better rates under weaker conditions](https://mlsanity.com/paper/1303.4645/) (2013)
- [A geometric alternative to Nesterov's accelerated gradient descent](https://mlsanity.com/paper/1506.08187/) (2015)
- [Tail-Sensitive KL and R'enyi Convergence of Unadjusted Hamiltonian Monte Carlo via One-Shot Couplings](https://mlsanity.com/paper/2601.09019/) (2026)
- [Improving Energy Conserving Descent for Machine Learning: Theory and Practice](https://mlsanity.com/paper/2306.00352/) (2023)
- [Hamiltonian Descent Methods](https://mlsanity.com/paper/1809.05042/) (2018)
- [Frictionless Hamiltonian Descent and Coordinate Hamiltonian Descent for Strongly Convex Quadratic Problems](https://mlsanity.com/paper/2402.13988/) (2024)

## Abstract (arXiv)

We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated convex optimization.