We use techniques from (tracial noncommutative) polynomial optimization to formulate
hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In …

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 deals with positive semidefinite matrix factorization (PS-DMF). PSDMF writes
each entry of a nonnegative matrix as the inner product of two symmetric positive …

Optimization is a fundamental area in mathematics and computer science, with many real-
world applications. In this thesis we study the efficiency with which we can solve certain …

Given a data matrix $ X\in\mathbb {R} _+^{m\times n} $ with non-negative entries, a Positive
Semidefinite (PSD) factorization of $ X $ is a collection of $ r\times r $-dimensional PSD …

The component-wise squared factorization decomposes a matrix as the component-wise
square of a low-rank matrix. It can be used to compute the so-called square root rank of a …

Suppose two separated parties, Alice and Bob, share a bipartite quantum state or a classical
correlation called a seed, and they try to generate a target classical correlation by …

We study properties of the central path underlying a nonlinear semidefinite optimization
problem, called NSDP for short. The latest radical work on this topic was contributed by …

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative
matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd …

We propose a primal-dual interior-point method (IPM) with convergence to second-order
stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as …