Solving bilevel programs with the KKT-approach

G. Bouza Allende; Georg J. Still

doi:10.1007/s10107-012-0535-x

Solving bilevel programs with the KKT-approach

G. Bouza Allende, Georg J. Still

Discrete Mathematics and Mathematical Programming

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97 Citations (Scopus)

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Abstract

Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.

Original language	English
Pages (from-to)	309-332
Number of pages	24
Journal	Mathematical programming
Volume	138
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-012-0535-x
Publication status	Published - 2013

Keywords

EWI-23989
IR-87879
METIS-300168
Bilevel problems · KKT-condition · FJ-condition · Mathematical programs with complementarity constraints · Genericity · Critical points

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10.1007/s10107-012-0535-x

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title = "Solving bilevel programs with the KKT-approach",

abstract = "Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.",

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AU - Bouza Allende, G.

AU - Still, Georg J.

N1 - Open Access

PY - 2013

Y1 - 2013

N2 - Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.

AB - Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.

KW - EWI-23989

KW - IR-87879

KW - METIS-300168

KW - Bilevel problems · KKT-condition · FJ-condition · Mathematical programs with complementarity constraints · Genericity · Critical points

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DO - 10.1007/s10107-012-0535-x

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VL - 138

SP - 309

EP - 332

JO - Mathematical programming

JF - Mathematical programming

IS - 1-2

ER -

Solving bilevel programs with the KKT-approach

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Keywords

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