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
209-225
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Vicente, Luis N.
32bf9328-ca05-497a-b201-a70c297d13c3
November 2006
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), .
(doi:10.1007/s10957-006-9136-2).
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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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
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Date deposited: 15 Oct 2007
Last modified: 16 Mar 2024 03:57
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Author:
Luis N. Vicente
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