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A semismooth newton-type method for bilevel programs with linear lower level problem

A semismooth newton-type method for bilevel programs with linear lower level problem
A semismooth newton-type method for bilevel programs with linear lower level problem

We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear constraints by means of a partial exact penalization. A regularized Newton system of equations is then generated from the latter problem and a Newton-type method is developed to solve it. Finally, we illustrate the practical implementation of the algorithm on the optimal toll-setting problem in transportation networks.

Bilevel optimization, Newton method, Optimal toll-setting
2189-3756
1437-1463
Kue, Floriane Mefo
c2971f52-f057-4549-ac12-8522e178d1a3
Raasch, Thorsten
d74c3a87-4327-4d17-b69a-3ca798d4ec05
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Kue, Floriane Mefo
c2971f52-f057-4549-ac12-8522e178d1a3
Raasch, Thorsten
d74c3a87-4327-4d17-b69a-3ca798d4ec05
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Kue, Floriane Mefo, Raasch, Thorsten and Zemkoho, Alain B. (2023) A semismooth newton-type method for bilevel programs with linear lower level problem. Pure and Applied Functional Analysis, 8 (5), 1437-1463.

Record type: Article

Abstract

We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear constraints by means of a partial exact penalization. A regularized Newton system of equations is then generated from the latter problem and a Newton-type method is developed to solve it. Finally, we illustrate the practical implementation of the algorithm on the optimal toll-setting problem in transportation networks.

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2010.11662v1 - Accepted Manuscript
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Accepted/In Press date: 22 October 2020
Published date: 2023
Related URLs:
Keywords: Bilevel optimization, Newton method, Optimal toll-setting

Identifiers

Local EPrints ID: 498992
URI: http://eprints.soton.ac.uk/id/eprint/498992
ISSN: 2189-3756
PURE UUID: 5ba26a2b-6625-48d9-ab3c-1c5134a57cd6
ORCID for Alain B. Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 06 Mar 2025 17:41
Last modified: 07 Mar 2025 02:47

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Contributors

Author: Floriane Mefo Kue
Author: Thorsten Raasch
Author: Alain B. Zemkoho ORCID iD

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