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

Benoit Colson, Patrice MARCOTTE, Gilles SAVARD

Research output: Book/Report/JournalOther report

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.
Original languageEnglish
Place of PublicationMontréal (QC), Canada
PublisherLes Cahiers du GERAD, G-2002-36 (Groupe d'Etudes et de Recherche en Analyse des Décisions, Ecole Polytechnique de Montréal)
Publication statusPublished - 2002

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

Keywords

  • bilevel programming
  • numerical results
  • approximation
  • trust-region methods
  • nonlinear programming

Cite this

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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keywords = "bilevel programming, numerical results, approximation, trust-region methods, nonlinear programming",
author = "Benoit Colson and Patrice MARCOTTE and Gilles SAVARD",
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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.

Research output: Book/Report/JournalOther report

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.