### Abstract

Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018). We also present an algorithm that finds these extra monomials for a given polynomial to yield an integral relaxation polytope or determines that no such set of extra monomials exists. In the former case, our approach yields an algorithm to solve the given polynomial optimization problem as a compact LP, and we complement this with a purely combinatorial algorithm.

Original language | English |
---|---|

Publisher | arXiv.org |

Number of pages | 27 |

Publication status | Published - 15 Nov 2019 |

### Publication series

Name | Arxiv.org |
---|---|

Publisher | Cornell University |

### Keywords

- cs.DM
- math.CO
- 90C57
- G.1.6; G.2.1

## Fingerprint Dive into the research topics of 'Integrality of Linearizations of Polynomials over Binary Variables using Additional Monomials'. Together they form a unique fingerprint.

## Cite this

Hojny, C., Pfetsch, M. E., & Walter, M. (2019).

*Integrality of Linearizations of Polynomials over Binary Variables using Additional Monomials*. (Arxiv.org). arXiv.org.