Hardness of some optimization problems over correlation polyhedra
Optimization and Control
2026-05-06 v1 Computational Complexity
Abstract
We prove the \textbf{NP}-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the rank-one matrices over . The problems are: membership, rank of the decomposition, and a ``relaxed rank'' obtained from relaxing the zero-norm expression for the rank to an norm. While membership and rank are natural problems for any matrix cone, the relaxed rank problem occurs in some signal processing and statistical applications.
Cite
@article{arxiv.2605.02896,
title = {Hardness of some optimization problems over correlation polyhedra},
author = {Alberto Caprara and Fabio Furini and Claudio Gentile and Leo Liberti and Andrea Lodi},
journal= {arXiv preprint arXiv:2605.02896},
year = {2026}
}