# Convergence rates of proximal gradient methods via the convex conjugate

arXiv: https://arxiv.org/abs/1801.02509 · HTML: https://mlsanity.com/paper/1801.02509/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization](https://mlsanity.com/paper/2111.11309/) (2021)
- [Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimization](https://mlsanity.com/paper/2305.17323/) (2023)

## Abstract (arXiv)

We give a novel proof of the O(1/k) and O(1/k2) convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function.