### Abstract

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newton-type methods for solving the problems. We show by a structural analysis that for (GSIP)-problems the regularity assumptions for the reduction approach can be expected to hold generically at a solution but for general (BL)-problems not. The genericity behavior of (BL) and (GSIP) is in particular studied for linear problems.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2000 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1544 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-90C30
- MSC-90C31
- IR-65731
- EWI-3364
- MSC-90C34

## Cite this

Stein, O., & Still, G. J. (2000).

*On generalized semi-infinite optimization and bilevel optimization*. Enschede: University of Twente, Department of Applied Mathematics.