On the Optimal Linear Minimization Oracle Complexity of Active-Hull Methods for Minimizing Convex Hölder Smooth Functions

We consider the convex problem $(P): {\min}_{y\in \mathbb{R}^n}\, f(Ay)+g(y)$, where $A:\mathbb{R}^n\to \mathbb{R}^m$ is a linear operator, $f$ is convex and $(M,ν)$-Hölder smooth on $\mathbb{R}^m$, and $g$ is proper, closed convex on $\mathbb{R}^n$, and admits a (generalized) linear minimization or