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I'm looking for a reference on how to sample uniformly (and preferably efficiently, elegantly, etc.) from the vertices of a polytope. I gather that enumerating vertices is hard. I also note the MO ...

Given the complete graph $K_n=(V,E)$, the Traveling Salesman Polytope is a convex polytope in $\Bbb R^E$ obtained as the convex hull of the indicator vectors of (edge-sets of) Hamiltonian cycles in $...

Given matrix $A \in \mathbb{R}^{m \times n}$ and vector $b \in \mathbb{R}^n$, consider the $\mathcal H$-polytope $P$ defined as follows $$ P := \left\{ x \in \mathbb{R}^n : Ax \leq b \right\} $$ I ...