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arXiv · 1812.10198

Perturbed Fenchel duality and first-order methods

David H. Gutman·Javier F. Peña
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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.

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David H. Gutman, Javier F. Peña. 2018-12-26. Perturbed Fenchel duality and first-order methods. https://arxiv.org/abs/1812.10198

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