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### Confusion related to k neighborly polytope

I was reading this paper related to neighborly polytope where they mentioned Consider a d×n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has many possible ...
I am computationally representing a convex polytope in $\mathbb{R}^n$ as a set $A$ of half-spaces that bound it; each such half-space is represented by a row vector $\mathbf{v} = \begin{bmatrix}v_1 ... 2answers 607 views ### Explain `All polyhedrons are convex sets´ My teacher in course in Mat-2.3140 of Aalto University claims that 'All polyhedrons are convex sets' here. This premise was in a false-or-not-problem 'The feasible set of linear integer problem is ... 1answer 51 views ### Are all polytopes also convex hulls? It seems, at least in the 2-D case, that all polytopes are going to be convex. Does this hold if the dimensions are increased? 1answer 205 views ###$L_1$projection of sum of convex functions onto polytopes Suppose I have a function$f(x) : \mathbb R^n \to \mathbb R$that is the sum of a given strictly convex function$g : \mathbb R \to \mathbb R$in a single variable, i.e.$f(x) = g(x_1) + g(x_2) + ...
Suppose one has a convex, bounded polytope P $\subset R^n$ and a strictly convex function $f$ defined everywhere on $R^n$. $f$ has a unique minimum; and suppose this minimum occurs somewhere strictly ...