The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

Gauss–Newton-type methods for bilevel optimization

Gauss–Newton-type methods for bilevel optimization
Gauss–Newton-type methods for bilevel optimization

This article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First, under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss–Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss–Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

Bilevel optimization, Gauss-Newton method, Partial exact penalization, Value function reformulation
0926-6003
793-824
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Tin, Andrey
9436c931-05ca-4354-9632-3c220a240877
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Tin, Andrey
9436c931-05ca-4354-9632-3c220a240877
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Fliege, Jörg, Tin, Andrey and Zemkoho, Alain (2021) Gauss–Newton-type methods for bilevel optimization. Computational Optimization and Applications, 78 (3), 793-824. (doi:10.1007/s10589-020-00254-3).

Record type: Article

Abstract

This article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First, under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss–Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss–Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

Text
Fliege2021_Article_GaussNewton-typeMethodsForBile - Version of Record
Available under License Creative Commons Attribution.
Download (932kB)
Other
Confirmation that output was published as OA
Restricted to Repository staff only
Request a copy

More information

Accepted/In Press date: 3 December 2020
e-pub ahead of print date: 10 January 2021
Published date: 1 April 2021
Keywords: Bilevel optimization, Gauss-Newton method, Partial exact penalization, Value function reformulation

Identifiers

Local EPrints ID: 448464
URI: http://eprints.soton.ac.uk/id/eprint/448464
ISSN: 0926-6003
PURE UUID: 1af5a3c9-5c34-44c1-b85e-4c597e242179
ORCID for Jörg Fliege: ORCID iD orcid.org/0000-0002-4459-5419
ORCID for Alain Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 22 Apr 2021 16:47
Last modified: 26 Nov 2021 03:03

Export record

Altmetrics

Contributors

Author: Jörg Fliege ORCID iD
Author: Andrey Tin
Author: Alain Zemkoho ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×