Perturbed Fenchel duality and first-order methods
Optimization and Control
2021-12-06 v7
Abstract
We show that the iterates generated by a generic first-order meta-algorithm satisfy a canonical perturbed Fenchel duality inequality. The latter in turn readily yields a unified derivation of the best known convergence rates for various popular first-order algorithms including the conditional gradient method as well as the main kinds of Bregman proximal methods: subgradient, gradient, fast gradient, and universal gradient methods.
Cite
@article{arxiv.1812.10198,
title = {Perturbed Fenchel duality and first-order methods},
author = {David H. Gutman and Javier F. Peña},
journal= {arXiv preprint arXiv:1812.10198},
year = {2021}
}
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26 pages