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 …

A game is played by a team of two—say Alice and Bob—in which the value of a random
variable x is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is …

We investigate the completely positive semidefinite cone CS_+^n, a new matrix cone
consisting of all n*n matrices that admit a Gram representation by positive semidefinite …

We study optimization programs given by a bilinear form over noncommutative variables
subject to linear inequalities. Problems of this form include the entangled value of two-prover …

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 …

An n * nn× n matrix X is called completely positive semidefinite (cpsd) if there exist d * dd× d
Hermitian positive semidefinite matrices {P_i\} _ i= 1^ n P ii= 1 n (for some d ≥ 1 d≥ 1) such …

A real symmetric matrix M is completely positive semidefinite if it admits a Gram
representation by (Hermitian) positive semidefinite matrices of any size d. The smallest such …

We analyze self-dual polyhedral cones and prove several properties about their slack
matrices. In particular, we show that self-duality is equivalent to the existence of a positive …

We investigate structural properties of the completely positive semidefinite cone $\mathcal
{CS} _+ $, consisting of all the $ n\times n $ symmetric matrices that admit a Gram …

We investigate structural properties of the completely positive semidefinite cone $\mathcal
{CS} _+^ n $, consisting of all the $ n\times n $ symmetric matrices that admit a Gram …