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Multicriteria approach to bilevel optimization

Multicriteria approach to bilevel optimization
Multicriteria approach to bilevel optimization
In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach.
bilevel optimization, multicriteria optimization
0022-3239
209-225
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Vicente, Luis N.
32bf9328-ca05-497a-b201-a70c297d13c3
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Vicente, Luis N.
32bf9328-ca05-497a-b201-a70c297d13c3

Fliege, Jörg and Vicente, Luis N. (2006) Multicriteria approach to bilevel optimization. Journal of Optimization Theory and Applications, 131 (2), 209-225. (doi:10.1007/s10957-006-9136-2).

Record type: Article

Abstract

In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach.

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More information

Published date: November 2006
Keywords: bilevel optimization, multicriteria optimization
Organisations: Operational Research

Identifiers

Local EPrints ID: 48819
URI: http://eprints.soton.ac.uk/id/eprint/48819
ISSN: 0022-3239
PURE UUID: 852a11cb-6ef3-4074-bf09-22c00b30d51f
ORCID for Jörg Fliege: ORCID iD orcid.org/0000-0002-4459-5419

Catalogue record

Date deposited: 15 Oct 2007
Last modified: 03 Dec 2019 01:44

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