All Questions

Let $C$ be a convex polytope in $\mathbb{R}^n$ with $m$ extremal points. Let $p\in \{1,2\}$. Can the $\ell^p$-projection $\Pi_C:\mathbb{R}^n\to C$ $$ \Pi_C(x) \in \operatorname{argmin}_{z\in C}\, \|x-...

Let $|\Sigma|$ be the underlying set of some fan $\Sigma$ in $\mathbb{R}^n$. It is well known that in general there is no coarsest fan structure on $|\Sigma|$. However, there may be some special rays ...

In tropical geometry, is there a notion of volume. Maybe one with some of the properties as found in classical convex geometry? If so, is there a good reference that elaborates on this question. I ...