# Generalized semi-infinite programming: A tutorial

Guerra Vázques, F. and Rückmann, J.-J. and Stein, O. and Still, G. (2008) *Generalized semi-infinite programming: A tutorial.* Journal of Computational and Applied Mathematics, 217 (2). pp. 394-419. ISSN 0377-0427

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Abstract: | This tutorial presents an introduction to generalized semi-infinite programming (GSIP) which in recent years became a vivid field of active research in mathematical programming. A GSIP problem is characterized by an infinite number of inequality constraints, and the corresponding index set depends additionally on the decision variables. There exist a wide range of applications which give rise to GSIP models; some of them are discussed in the present paper. Furthermore, geometric and topological properties of the feasible set and, in particular, the difference to the standard semi-infinite case are analyzed. By using first-order approximations of the feasible set corresponding constraint qualifications are developed. Then, necessary and sufficient first- and second-order optimality conditions are presented where directional differentiability properties of the optimal value function of the so-called lower level problem are used. Finally, an overview of numerical methods is given. |

Item Type: | Article |

Copyright: | © 2008 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/62581 |

Official URL: | http://dx.doi.org/10.1016/j.cam.2007.02.012 |

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