Title | Interval Methods for Semi-infinite Programs", , 30(1):63-93, 2005 |

Publication Type | Journal Article |

Year of Publication | 2005 |

Authors | Bhattacharjee B, Lemonidis P, Green WH, Barton PI |

Journal | Computational Optimization and Applications |

Volume | 30 |

Pagination | 63-93 |

Keywords | global optimization, interval analysis, semi-infinite programming |

Abstract | A new approach for the numerical solution of smooth, nonlinear semi-infinite programs whose feasible set contains a nonempty interior is presented. Interval analysis methods are used to construct finite nonlinear, or mixed-integer nonlinear, reformulations of the original semi-infinite program under relatively mild assumptions on the problem structure. In certain cases the finite reformulation is exact and can be solved directly for the global minimum of the semi-infinite program ({SIP}). In the general case, this reformulation is over-constrained relative to the {SIP}, such that solving it yields a guaranteed feasible upper bound to the {SIP} solution. This upper bound can then be refined using a subdivision procedure which is shown to converge to the true {SIP} solution with finite egr-optimality. In particular, the method is shown to converge for {SIPs} which do not satisfy regularity assumptions required by reduction-based methods, and for which certain points in the feasible set are subject to an infinite number of active constraints. Numerical results are presented for a number of problems in the {SIP} literature. The solutions obtained are compared to those identified by reduction-based methods, the relative performances of the nonlinear and mixed-integer nonlinear formulations are studied, and the use of different inclusion functions in the finite reformulation is investigated. |

URL | http://dx.doi.org/10.1007/s10589-005-4556-8 |

DOI | 10.1007/s10589-005-4556-8 |

# Interval Methods for Semi-infinite Programs", , 30(1):63-93, 2005

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