## Abstract

Linear programming is a basic mathematical technique for optimizing a linear function on a domain that is constrained by linear inequalities. We restrict ourselves to linear programs on bounded domains that involve only real variables. In the context of theorem proving, this restriction makes it possible for any given linear program to obtain certificates from external linear programming tools that help to prove arbitrarily precise bounds for the given linear program. To this end, an explicit formalization of matrices in Isabelle/HOL is presented, and how the concept of lattice-ordered rings allows for a smooth integration of matrices with the axiomatic type classes of Isabelle.

As our work is a contribution to the Flyspeck project, we argue that with the above techniques it is now possible to prove bounds for the linear programs arising in the proof of the Kepler conjecture sufficiently fast.

As our work is a contribution to the Flyspeck project, we argue that with the above techniques it is now possible to prove bounds for the linear programs arising in the proof of the Kepler conjecture sufficiently fast.

Original language | English |
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Title of host publication | Theorem Proving in Higher Order Logics |

Subtitle of host publication | 18th International Conference, TPHOLs 2005, Oxford, UK, August 22-25, 2005. Proceedings |

Editors | Joe Hurd, Tom Melham |

Publisher | Springer Berlin Heidelberg |

Pages | 227-244 |

Number of pages | 18 |

ISBN (Electronic) | 978-3-540-31820-0 |

ISBN (Print) | 978-3-540-28372-0 |

DOIs | |

Publication status | Published - 2005 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Berlin Heidelberg |

Number | 3603 |

ISSN (Print) | 0302-9743 |