### Abstract

Original language | English |
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Place of Publication | Ithaca |

Publisher | Cornell University Library |

Number of pages | 29 |

Publication status | Published - Dec 2018 |

### Publication series

Name | arXiv |
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Volume | 1812.00274 |

### Fingerprint

### Cite this

*Positive semidefinite approximations to the cone of copositive kernels*. (arXiv; Vol. 1812.00274). Ithaca: Cornell University Library.

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**Positive semidefinite approximations to the cone of copositive kernels.** / Kuryatnikova, Olga; Vera, J. C.

Research output: Working paper › Other research output

TY - UNPB

T1 - Positive semidefinite approximations to the cone of copositive kernels

AU - Kuryatnikova, Olga

AU - Vera, J. C.

PY - 2018/12

Y1 - 2018/12

N2 - It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional cone is not tractable, and approximations of this cone have been hardly considered in literature. We propose two convergent hierarchies of subsets of copositive kernels, in terms of non-negative and positive definite kernels. We use these hierarchies and representation theorems for invariant positive definite kernels on the sphere to construct new SDP-based bounds on the kissing number. This results in fast-to-compute upper bounds on the kissing number that lie between the currently existing LP and SDP bounds.

AB - It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional cone is not tractable, and approximations of this cone have been hardly considered in literature. We propose two convergent hierarchies of subsets of copositive kernels, in terms of non-negative and positive definite kernels. We use these hierarchies and representation theorems for invariant positive definite kernels on the sphere to construct new SDP-based bounds on the kissing number. This results in fast-to-compute upper bounds on the kissing number that lie between the currently existing LP and SDP bounds.

M3 - Working paper

T3 - arXiv

BT - Positive semidefinite approximations to the cone of copositive kernels

PB - Cornell University Library

CY - Ithaca

ER -