Abstract Let M ∈ R^ p * q M∈ R p× q be a nonnegative matrix. The positive semidefinite
rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite …

We develop a framework for proving approximation limits of polynomial size linear programs
(LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This …

We study the convex hull of SO(n), the set of n*n orthogonal matrices with unit determinant,
from the point of view of semidefinite programming. We show that the convex hull of SO(n) is …

Let A be an m*n matrix with nonnegative real entries. The PSD rank of A is the smallest
integer k for which there exist k*k real PSD matrices B_1,...,B_m, C_1,...,C_n satisfying …

The second-order cone plays an important role in convex optimization and has strong
expressive abilities despite its apparent simplicity. Second-order cone formulations can also …

Let A be an m× n matrix with nonnegative real entries. The psd rank of A is the smallest k for
which there exist two families (P 1,…, P m) and (Q 1,…, Q n) of positive semidefinite …

This paper considers the problem of positive semidefinite factorization (PSD factorization), a
generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative …

arxiv:1412.0728v2 [math.CO] 29 Feb 2020 Page 1 SUBLINEAR EXTENSIONS OF POLYGONS
YAROSLAV SHITOV Abstract. Every convex polygon with n vertices is a linear projection of a …

We consider the problem of finding the smallest rank of a complex matrix whose absolute
values of the entries are given. We call this minimum the phaseless rank of the matrix of the …

We show that every heptagon is a section of a $3 $-polytope with $6 $ vertices. This implies
that every $ n $-gon with $ n\geq 7$ can be obtained as a section of a $(2+\lfloor\frac …