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Extension of the value function reformulation to multiobjective bilevel optimization

Extension of the value function reformulation to multiobjective bilevel optimization
Extension of the value function reformulation to multiobjective bilevel optimization
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used to deal with the lower-level problem. Here, we utilize the concept of frontier map that extends the notion of optimal value function to our parametric multiobjective lower-level problem. Based on this, we build a tractable constraint qualification that we use to derive necessary optimality conditions for the problem. Subsequently, we show that our resulting necessary optimality conditions represent a natural extension from standard optimistic bilevel programs with scalar objective functions.
Coderivative, Frontier map, Multiobjective bilevel optimization, Optimality conditions, Strong domination property
1862-4472
Lafhim, Lahoussine
91f799b8-61c7-4ed6-b8f1-ccf6b6e220fc
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Lafhim, Lahoussine
91f799b8-61c7-4ed6-b8f1-ccf6b6e220fc
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Lafhim, Lahoussine and Zemkoho, Alain (2022) Extension of the value function reformulation to multiobjective bilevel optimization. Optimization Letters, 2022. (doi:10.1007/s11590-022-01948-9).

Record type: Article

Abstract

We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used to deal with the lower-level problem. Here, we utilize the concept of frontier map that extends the notion of optimal value function to our parametric multiobjective lower-level problem. Based on this, we build a tractable constraint qualification that we use to derive necessary optimality conditions for the problem. Subsequently, we show that our resulting necessary optimality conditions represent a natural extension from standard optimistic bilevel programs with scalar objective functions.

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Accepted/In Press date: 19 October 2022
e-pub ahead of print date: 28 October 2022
Published date: 28 October 2022
Additional Information: Funding Information: The work of AZ is supported by the EPSRC grant EP/V049038/1 and the Alan Turing Institute for Data Science and Artificial Intelligence under the EPSRC grant EP/N510129/1 Publisher Copyright: © 2022, The Author(s).
Keywords: Coderivative, Frontier map, Multiobjective bilevel optimization, Optimality conditions, Strong domination property

Identifiers

Local EPrints ID: 471995
URI: http://eprints.soton.ac.uk/id/eprint/471995
ISSN: 1862-4472
PURE UUID: 88114a3a-09ed-4093-b879-a89ca647c5ec
ORCID for Alain Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

Catalogue record

Date deposited: 23 Nov 2022 17:46
Last modified: 17 Mar 2024 03:37

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Contributors

Author: Lahoussine Lafhim
Author: Alain Zemkoho ORCID iD

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