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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Communicated by P. M. Pardalos
This paper was completed while the author was on leave at the Institute of Applied Mathematics, University of Erlangen-Nürnberg, Germany
Support for this author was provided by Centro de Matemática da Universidade de Coimbra, by FCT under Grant POCTI/35059/MAT/2000, by the European Union under Grant IST-2000-26063, and by Fundação Calouste Gulbenkian. The author also thanks the IBM T.J. Watson Research Center and the Institute for Mathematics and Its Applications for their local support
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Fliege, J., Vicente, L.N. Multicriteria Approach to Bilevel Optimization. J Optim Theory Appl 131, 209–225 (2006). https://doi.org/10.1007/s10957-006-9136-2
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DOI: https://doi.org/10.1007/s10957-006-9136-2