Title | Semi-Infinite Optimization With Implicit Functions |

Publication Type | Journal Article |

Year of Publication | 2015 |

Authors | Stuber MD, Barton PI |

Journal | Ind. Eng. Chem. Res. |

Volume | 54 |

Issue | 1 |

Pagination | 307–317 |

Date Published | 01/2015 |

Abstract | In this work, equality-constrained bilevel optimization problems, arising from engineering design, economics, and operations research problems, are reformulated as an equivalent semi-infinite program (SIP) with implicit functions embedded, which are defined by the original equality constraints that model the system. Using recently developed theoretical tools for bounding implicit functions, a recently developed algorithm for global optimization of implicit functions, and a recently developed algorithm for solving standard SIPs with explicit functions to global optimality, a method for solving SIPs with implicit functions embedded is presented. The method is guaranteed to converge to epsilon-optimality in finitely many iterations given the existence of a Slater point arbitrarily close to a minimizer. Besides the Slater point assumption, it is assumed only that the functions are continuous and factorable, and that the model equations are once continuously differentiable. |

URL | http://pubs.acs.org/doi/abs/10.1021/ie5029123 |

DOI | 10.1021/ie5029123 |

# Semi-Infinite Optimization With Implicit Functions

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