# Convergence of first-order methods via the convex conjugate

arXiv: https://arxiv.org/abs/1707.09084 · HTML: https://mlsanity.com/paper/1707.09084/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimization](https://mlsanity.com/paper/2305.17323/) (2023)

## Abstract (arXiv)

This paper gives a unified and succinct approach to the O(1/√k), O(1/k), and O(1/k2) convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function.