Multicriteria approach to bilevel optimization

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Authors

Colleges, School and Institutes

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.

Details

Original languageEnglish
Pages (from-to)209-225
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume131
Issue number2
Publication statusPublished - 1 Nov 2006

Keywords

  • multicriteria optimization, bilevel optimization