On generalized semi-infinite optimization and bilevel optimization

Oliver Stein; Georg J. Still

doi:10.1016/S0377-2217(01)00307-1

On generalized semi-infinite optimization and bilevel optimization

Oliver Stein
, Georg J. Still

Discrete Mathematics and Mathematical Programming

Research output: Contribution to journal › Article › Academic › peer-review

79 Citations (Scopus)

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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 language	English
Pages (from-to)	444-462
Journal	European journal of operational research
Volume	142
Issue number	3
DOIs	https://doi.org/10.1016/S0377-2217(01)00307-1
Publication status	Published - 2002

Keywords

IR-74650
METIS-208601
Genericity behavior
Optimality conditions
Numerical methods
Semi-infinite programming
Bilevel programming

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10.1016/S0377-2217(01)00307-1

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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.",

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AU - Stein, Oliver

AU - Still, Georg J.

PY - 2002

Y1 - 2002

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 - IR-74650

KW - METIS-208601

KW - Genericity behavior

KW - Optimality conditions

KW - Numerical methods

KW - Semi-infinite programming

KW - Bilevel programming

U2 - 10.1016/S0377-2217(01)00307-1

DO - 10.1016/S0377-2217(01)00307-1

M3 - Article

SN - 0377-2217

VL - 142

SP - 444

EP - 462

JO - European journal of operational research

JF - European journal of operational research

IS - 3

ER -

On generalized semi-infinite optimization and bilevel optimization

Abstract

Keywords

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