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Jul 19, 2019 at 14:59 answer added Ivan Izmestiev timeline score: 2
Jul 19, 2019 at 12:12 history edited user136604 CC BY-SA 4.0
Added condition that $P$ is full-dimensional.
Jul 19, 2019 at 12:07 comment added user136604 Also, I should mention that I am interested in full dimensional polyhedra $P \subset \mathbb{R}^n$, i.e, $dim(P)=n$... so existence of a function that is strictly convex across codimension one simplexes makes sense.
Jul 19, 2019 at 12:04 comment added user136604 There exists a point $p\in int(P)$ such that for any $x\in P$, the interior of the line segment $[x,p]$ joining $x$ and $p$, lies in the interior of $P$.
Jul 19, 2019 at 11:01 comment added Joseph O'Rourke Could you please define "star-convex"?
Jul 19, 2019 at 9:54 history asked user136604 CC BY-SA 4.0