# Dynamic behavior for a gradient algorithm with energy and momentum

arXiv: https://arxiv.org/abs/2203.12199 · HTML: https://mlsanity.com/paper/2203.12199/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2022.

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

- [SGEM: stochastic gradient with energy and momentum](https://mlsanity.com/paper/2208.02208/) (2022)
- [Accelerating Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2504.03158/) (2025)

## Abstract (arXiv)

This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly boundedness and convergence to critical points, are examined. The dynamic behavior is studied through a comprehensive analysis of a high-resolution ODE system. This ODE system, being nonlinear, is derived by taking the limit of the discrete scheme while preserving the momentum effect through a rescaling of the momentum parameter. The paper emphasizes the global well-posedness of the ODE system and the time-asymptotic convergence of solution trajectories. Furthermore, we establish a linear convergence rate for objective functions that adhere to the Polyak-Lojasiewicz condition.