# Convergences Rates of Proximal Gradient Methods via the Convex Conjugate

David Gutman, Javier Pena

Research output: Contribution to journalArticle

### Abstract

We give a novel proof of the ${{\mathcal O}}(1/k)$ and ${{\mathcal O}}(1/k^2)$ 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.
Original language English 162-174 SIAM Journal on Optimization https://doi.org/10.1137/18M1164329 Published - Jan 17 2019