@article{4c5afc60af8c4b7d96b1f5e2a8fc180f,
title = "Lower bounds on matrix factorization ranks via noncommutative polynomial optimization",
abstract = "We use techniques from (tracial noncommutative) polynomial optimization to formu-late hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank,and their symmetric analogs: the completely positive rank and the completely positive semidefinite rank. We study convergence properties of our hierarchies, compare themextensively to known lower bounds, and provide some (numerical) examples.",
keywords = "Matrix factorization ranks, Nonnegative rank Positive semidefinite rank, Completely positive rank, Completely positive semidefinite rank, Noncommutative polynomial optimization",
author = "Sander Gribling and {De Laat}, David and Monique Laurent",
year = "2019",
month = oct,
doi = "10.1007/s10208-018-09410-y",
language = "English",
volume = "19",
pages = "1013--1070",
journal = "Foundations of Computational Mathematics",
issn = "1615-3375",
publisher = "Springer New York",
number = "5",
}