Newton-type method for bilevel programs with linear lower level problem and application to toll optimization
Newton-type method for bilevel programs with linear lower level problem and application to toll optimization
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 semismooth system of equations is then generated from the later problem and a Newton-type method is developed to solve it. Finally, we illustrate the convergence and practical implementation of the algorithm on the optimal toll-setting problem in transportation networks.
math.OC
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.
(2020)
Newton-type method for bilevel programs with linear lower level problem and application to toll optimization.
arXiv.
(In Press)
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 semismooth system of equations is then generated from the later problem and a Newton-type method is developed to solve it. Finally, we illustrate the convergence and practical implementation of the algorithm on the optimal toll-setting problem in transportation networks.
Text
2010.11662v1
- Accepted Manuscript
Available under License Other.
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Accepted/In Press date: 22 October 2020
Keywords:
math.OC
Identifiers
Local EPrints ID: 508443
URI: http://eprints.soton.ac.uk/id/eprint/508443
ISSN: 2331-8422
PURE UUID: 5b8e1ab7-42cd-4219-8f26-72dcd957d2ee
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Date deposited: 21 Jan 2026 17:50
Last modified: 22 Jan 2026 02:46
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Author:
Floriane Mefo Kue
Author:
Thorsten Raasch
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