## Abstract

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min-max stochastic queue location problem are reported.

Original language | English (US) |
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Pages (from-to) | 83-108 |

Number of pages | 26 |

Journal | Mathematical Programming |

Volume | 63 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1994 |

## Keywords

- Convex programming
- deep cut ellipsoid algorithm
- location theory
- min-max programming
- rate of convergence