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Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization

Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization
Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization
We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg-Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem, we conduct a careful experimental study to this effect, in the context the Levenberg-Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems.
math.OC
2331-8422
Tin, Andrey
9436c931-05ca-4354-9632-3c220a240877
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Tin, Andrey
9436c931-05ca-4354-9632-3c220a240877
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Tin, Andrey and Zemkoho, Alain B. (2021) Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization. arXiv.

Record type: Article

Abstract

We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg-Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem, we conduct a careful experimental study to this effect, in the context the Levenberg-Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems.

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2101.09521v1 - Accepted Manuscript
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More information

Accepted/In Press date: 23 January 2021
e-pub ahead of print date: 23 January 2021
Published date: 23 January 2021
Keywords: math.OC

Identifiers

Local EPrints ID: 448047
URI: http://eprints.soton.ac.uk/id/eprint/448047
ISSN: 2331-8422
PURE UUID: c946c013-9393-456a-9426-3bf422c90d88
ORCID for Alain B. Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 01 Apr 2021 15:39
Last modified: 17 Apr 2021 01:48

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Contributors

Author: Andrey Tin

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