5 papers
Facial distance and diameter
Antoine Deza, David Martínez-Rubio, Javier Peña +1
The facial distance of a polytope, equivalently its pyramidal width, is a geometric condition measure that appears in the convergence bounds for Frank--Wolfe algorithms. Peña and W…
Calculus of the Facial Distance
Javier Pena, Elias Wirth
We develop a few calculus rules to compute or lower bound the facial distance of a polytope. We illustrate our calculus rules on various popular polytopes. In particular, we provid…
Adaptive Open-Loop Step-Sizes for Accelerated Convergence Rates of the Frank-Wolfe Algorithm
Elias Wirth, Javier Peña, Sebastian Pokutta
Recent work has shown that in certain settings, the Frank-Wolfe algorithm (FW) with open-loop step-sizes for a fixed parameter $\ell \in \mathbb{N},\, \…
Fast convergence of Frank-Wolfe algorithms on polytopes
Elias Wirth, Javier Pena, Sebastian Pokutta
We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Fr…
Accelerated Affine-Invariant Convergence Rates of the Frank-Wolfe Algorithm with Open-Loop Step-Sizes
Elias Wirth, Javier Pena, Sebastian Pokutta
Recent papers have shown that the Frank-Wolfe algorithm (FW) with open-loop step-sizes exhibits rates of convergence faster than the iconic rate. In particula…