On generalized semi-infinite optimization and bilevel optimization

O. Stein, Georg J. Still

Research output: Book/ReportReportOther research output

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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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2000

Publication series

Name
PublisherDepartment 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.
Stein, O. ; Still, Georg J. / On generalized semi-infinite optimization and bilevel optimization. Enschede : University of Twente, Department of Applied Mathematics, 2000.
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Stein, O & Still, GJ 2000, On generalized semi-infinite optimization and bilevel optimization. University of Twente, Department of Applied Mathematics, Enschede.

On generalized semi-infinite optimization and bilevel optimization. / Stein, O.; Still, Georg J.

Enschede : University of Twente, Department of Applied Mathematics, 2000.

Research output: Book/ReportReportOther research output

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T1 - On generalized semi-infinite optimization and bilevel optimization

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AU - Still, Georg J.

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N2 - 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.

AB - 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.

KW - MSC-90C30

KW - MSC-90C31

KW - IR-65731

KW - EWI-3364

KW - MSC-90C34

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BT - On generalized semi-infinite optimization and bilevel optimization

PB - University of Twente, Department of Applied Mathematics

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Stein O, Still GJ. On generalized semi-infinite optimization and bilevel optimization. Enschede: University of Twente, Department of Applied Mathematics, 2000.