A note on partial calmness for bilevel optimization problems with linearly structured lower level
A note on partial calmness for bilevel optimization problems with linearly structured lower level
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush–Kuhn–Tucker-type necessary optimality conditions in order to characterize local minimizers. In the past, sufficient conditions for the validity of partial calmness have been investigated. In this regard, the presence of a linearly structured lower level problem has turned out to be beneficial. However, the associated literature suffers from inaccurate results. In this note, we clarify some regarding erroneous statements and visualize the underlying issues with the aid of illustrative counterexamples.
Bilevel optimization, Linear programming, Partial calmness
Mehlitz, Patrick
eecbbf4c-dc3f-44d5-b448-3053f23874f4
Minchenko, Leonid
873c8718-9518-4ecd-9009-dff583c1c54f
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
16 September 2020
Mehlitz, Patrick
eecbbf4c-dc3f-44d5-b448-3053f23874f4
Minchenko, Leonid
873c8718-9518-4ecd-9009-dff583c1c54f
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Mehlitz, Patrick, Minchenko, Leonid and Zemkoho, Alain
(2020)
A note on partial calmness for bilevel optimization problems with linearly structured lower level.
Optimization Letters.
(doi:10.1007/s11590-020-01636-6).
Abstract
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush–Kuhn–Tucker-type necessary optimality conditions in order to characterize local minimizers. In the past, sufficient conditions for the validity of partial calmness have been investigated. In this regard, the presence of a linearly structured lower level problem has turned out to be beneficial. However, the associated literature suffers from inaccurate results. In this note, we clarify some regarding erroneous statements and visualize the underlying issues with the aid of illustrative counterexamples.
Text
2003.06138
- Accepted Manuscript
More information
Accepted/In Press date: 19 August 2020
Published date: 16 September 2020
Keywords:
Bilevel optimization, Linear programming, Partial calmness
Identifiers
Local EPrints ID: 444584
URI: http://eprints.soton.ac.uk/id/eprint/444584
ISSN: 1862-4472
PURE UUID: 87a060d2-76d7-4166-a64d-71f07bb819ec
Catalogue record
Date deposited: 26 Oct 2020 17:32
Last modified: 17 Mar 2024 05:59
Export record
Altmetrics
Contributors
Author:
Patrick Mehlitz
Author:
Leonid Minchenko
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
