Work

Hardness of some optimization problems over correlation polyhedra

Year: 2026

Type: preprint

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 $n\times n$ rank-one matrices over $\{0,1\}$. The problems are: membership, rank of the decomposition, and a ``relaxed rank'' obtained from relaxing the zero-norm expression for the rank to an $\ell_1$ norm. While membership and rank are natural problems for any matrix cone, the relaxed rank problem occurs in some signal processing and statistical applications.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.02896

Authors: Caprara, Alberto, Furini, Fabio, Gentile, Claudio, Liberti, Leo, Lodi, Andrea

Institutions: University of Bologna, CI2, Sapienza University of Rome, Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti, Centre National de la Recherche Scientifique, Laboratoire d'Informatique de l'École Polytechnique, Cornell University, Cortech Solutions (United States)

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Istituto Nazionale di Alta Matematica "Francesco Severi"

Award: G7103356121

OpenAlex ID: W7160417644

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