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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
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
1862-4472
Mehlitz, Patrick
eecbbf4c-dc3f-44d5-b448-3053f23874f4
Minchenko, Leonid
873c8718-9518-4ecd-9009-dff583c1c54f
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
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).

Record type: Article

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.

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2003.06138 - Accepted Manuscript
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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
ORCID for Alain Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 26 Oct 2020 17:32
Last modified: 26 Nov 2021 06:39

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Contributors

Author: Patrick Mehlitz
Author: Leonid Minchenko
Author: Alain Zemkoho ORCID iD

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