Adaptive Accelerated Gradient Method for Smooth Convex Optimization

Fuente: arXiv
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Main Authors: Wang, Zepeng, Peypouquet, Juan
Format: Preprint
Published: 2025
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author Wang, Zepeng
Peypouquet, Juan
author_facet Wang, Zepeng
Peypouquet, Juan
contents 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 $\mathcal{O}\left( \frac{1}{k^2} \right)$. Moreover, if the objective function is strongly convex, the function values converge at a linear rate.
format Preprint
id arxiv_https___arxiv_org_abs_2512_20478
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Adaptive Accelerated Gradient Method for Smooth Convex Optimization
Wang, Zepeng
Peypouquet, Juan
Optimization and Control
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 $\mathcal{O}\left( \frac{1}{k^2} \right)$. Moreover, if the objective function is strongly convex, the function values converge at a linear rate.
title Adaptive Accelerated Gradient Method for Smooth Convex Optimization
topic Optimization and Control
url https://arxiv.org/abs/2512.20478