Adaptive Accelerated Gradient Descent Methods for Convex Optimization
Optimization and Control
2026-02-10 v2
Abstract
This work proposes AGD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the method triggers line search only when accumulated perturbations become positive, thereby reducing gradient evaluations while preserving strong convergence guarantees. By integrating adaptive step size and momentum acceleration, AGD outperforms existing first-order methods across a range of problem settings.
Cite
@article{arxiv.2601.19013,
title = {Adaptive Accelerated Gradient Descent Methods for Convex Optimization},
author = {Zeyi Xu and Long Chen},
journal= {arXiv preprint arXiv:2601.19013},
year = {2026}
}