A trust-region method for nonlinear bilevel programming: algorithm and computational experience

Benoit Colson, Patrice MARCOTTE, Gilles SAVARD

Résultats de recherche: Livre/Rapport/RevueAutre rapport

Résumé

Nous considérons l'approximation de programmes mathématiques à deux niveaux par des problèmes résolubles du même type, c'est-à-dire des problèmes bi-niveaux avec une approximation linéaire de l'objectif de premier niveau et de toutes les contraintes et une approximation quadratique de la fonction objectif de second niveau. Nous décrivons les principales caractéristiques de l'algorithme et le logiciel qui l'accompagne. Les résultats numériques préliminaires semblent confirmer le caractère remarquable de la méthode.
langue originaleAnglais
Lieu de publicationMontréal (QC), Canada
EditeurLes Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal)
étatPublié - 2002

Empreinte digitale

Bilevel Programming
Trust Region Method
Nonlinear Programming
Quadratic Approximation
Linear Approximation
Numerical Experiment
Tend
Software
Approximation
Experience

Citer ceci

Colson, B., MARCOTTE, P., & SAVARD, G. (2002). A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Montréal (QC), Canada: Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal).
Colson, Benoit ; MARCOTTE, Patrice ; SAVARD, Gilles. / A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Montréal (QC), Canada : Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal), 2002.
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title = "A trust-region method for nonlinear bilevel programming: algorithm and computational experience",
abstract = "We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Preliminary numerical experiments tend to confirm the remarkable behavior of the method.",
keywords = "bilevel programming, numerical results, approximation, trust-region methods, nonlinear programming",
author = "Benoit Colson and Patrice MARCOTTE and Gilles SAVARD",
year = "2002",
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Colson, B, MARCOTTE, P & SAVARD, G 2002, A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal), Montréal (QC), Canada.

A trust-region method for nonlinear bilevel programming: algorithm and computational experience. / Colson, Benoit; MARCOTTE, Patrice; SAVARD, Gilles.

Montréal (QC), Canada : Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal), 2002.

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

T1 - A trust-region method for nonlinear bilevel programming: algorithm and computational experience

AU - Colson, Benoit

AU - MARCOTTE, Patrice

AU - SAVARD, Gilles

PY - 2002

Y1 - 2002

N2 - We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Preliminary numerical experiments tend to confirm the remarkable behavior of the method.

AB - We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Preliminary numerical experiments tend to confirm the remarkable behavior of the method.

KW - bilevel programming

KW - numerical results

KW - approximation

KW - trust-region methods

KW - nonlinear programming

M3 - Other report

BT - A trust-region method for nonlinear bilevel programming: algorithm and computational experience

PB - Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal)

CY - Montréal (QC), Canada

ER -

Colson B, MARCOTTE P, SAVARD G. A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Montréal (QC), Canada: Les Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal), 2002.