### Abstract

In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the optimal solution of some infinite-dimensional copositive program. For this we develop a duality theory between the primal convex cone of copositive kernels and the dual convex cone of completely positive measures. We determine the extreme rays of the latter cone, and we illustrate this theory with the help of the kissing number problem.

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

Pages (from-to) | 65-83 |

Journal | Mathematical Programming |

Volume | 160 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

### Keywords

- Completely positive cone of measures
- Copositive cone of continuous Hilbert-Schmidt kernels
- Extreme rays
- Stability number

## Fingerprint Dive into the research topics of 'A copositive formulation for the stability number of infinite graphs'. Together they form a unique fingerprint.

## Cite this

*Mathematical Programming*,

*160*(1), 65-83. https://doi.org/10.1007/s10107-015-0974-2