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
Lafhim, Lahoussine
91f799b8-61c7-4ed6-b8f1-ccf6b6e220fc
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
28 October 2022
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).
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.
Text
s11590-022-01948-9
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More information
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
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Date deposited: 23 Nov 2022 17:46
Last modified: 17 Mar 2024 03:37
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Author:
Lahoussine Lafhim
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