2019/11/30 by Radu-Alexandru Dragomir, Adrien Taylor, Alexandre d'Aspremont +1 · 1 citation
Mathematics · Computer Science · #math.OC #cs.NA #math.NA #msc:90C25 #msc:90C06 #msc:90C60 #msc:90C22 #msc:68Q25
paper · pdf · doi:10.1007/s10107-021-01618-1
To appear in Mathematical Programming
arxiv created 2021/02/17 · arxiv updated 2021/02/18
We provide a lower bound showing that the O(1/k) convergence rate of the NoLips method (a.k.a. Bregman Gradient) is optimal for the class of functions satisfying the h-smoothness assumption. This assumption, also known as relative smoothness, appeared in the recent developments around the Bregman Gradient method, where acceleration remained an open issue. On the way, we show how to constructively obtain the corresponding worst-case functions by extending the computer-assisted performance estimation framework of Drori and Teboulle (Mathematical Programming, 2014) to Bregman first-order methods, and to handle the classes of differentiable and strictly convex functions.