English

Adaptive Accelerated Gradient Method for Smooth Convex Optimization

Optimization and Control 2025-12-24 v1

Abstract

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence generated by this method converges weakly to a minimizer of the objective function, and the function values converge at a fast rate of O(1k2)\mathcal{O}\left( \frac{1}{k^2} \right). Moreover, if the objective function is strongly convex, the function values converge at a linear rate.

Keywords

Cite

@article{arxiv.2512.20478,
  title  = {Adaptive Accelerated Gradient Method for Smooth Convex Optimization},
  author = {Zepeng Wang and Juan Peypouquet},
  journal= {arXiv preprint arXiv:2512.20478},
  year   = {2025}
}