# The Multilinear Polytope for Acyclic Hypergraphs

@article{Pia2018TheMP,
title={The Multilinear Polytope for Acyclic Hypergraphs},
author={Alberto Del Pia and Aida Khajavirad},
journal={SIAM J. Optim.},
year={2018},
volume={28},
pages={1049-1076}
}
• Published 10 April 2018
• Mathematics
• SIAM J. Optim.
We consider the multilinear polytope defined as the convex hull of the set of binary points $z$ satisfying a collection of equations of the form $z_e = \prod_{v \in e} {z_v}$, $e \in E$, where $E$ denotes a family of subsets of $\{1, \ldots , n\}$ of cardinality at least two. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as $0-1$ polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial…

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