1
vote
0answers
13 views

Extra information needed to distinguish combinatorially isomorphic polytopes

The title pretty much sums up my question: what extra information do we need (or what is an example of sufficient information) on top of the face lattice in order to completely characterize a convex ...
1
vote
0answers
57 views

Confusion related to k neighborly polytope

I was reading this paper related to neighborly polytope where they mentioned: Consider a $d \times n$ matrix $A$, with $d < n$. The problem of solving for $x$ in $y = Ax$ is underdetermined, ...
1
vote
1answer
137 views

Submodularity of the product of two non-negative, monotone increasing submodular functions

I'm trying to prove the submodularity of the product of two non-negative, monotone increasing submodular functions Formally, we have $f$ and $g$ are submodular functions, that is, ...
3
votes
1answer
58 views

Convex programming when the problem has an underlying combinatorial structure that's a DAG

I have a nonlinear convex objective function to minimize. The function is defined on a set of variables: $\{ x_1,x_2, \ldots ,x_p \},$ where each $x_i$ is a number associated with a path in the DAG. ...
4
votes
2answers
180 views

Is the rising factorial function a convex function?

Let $(x)_p=x(x+1)\dots(x+p-1)$ be the rising factorial function. My question is: Is $(x)_p$ a convex function or not? And how to proof? And what is about the falling factorial function ...