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Methods for Multiobjective Bilevel Optimization

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Bilevel Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 161))

Abstract

This chapter is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems by means of scalarization functionals and optimality conditions. These can be used in theoretical and numerical approaches to multiobjective bilevel optimization.

As multiple objectives arise in multiobjective optimization as well as in bilevel optimization problems, we also point out the results on the connection between these two classes of optimization problems. Finally, we give reference to numerical approaches which have been followed in the literature to solve these kind of problems. We concentrate in this chapter on nonlinear problems, while the results and statements naturally also hold for the linear case.

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Authors and Affiliations

  1. Institute for Mathematics, TU Ilmenau, Ilmenau, Germany

    Gabriele Eichfelder

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  1. Gabriele Eichfelder
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Correspondence to Gabriele Eichfelder .

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Editors and Affiliations

  1. Institute of Numerical Mathematics and Optimization, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

  2. School of Mathematical Sciences, University of Southampton, Southampton, UK

    Alain Zemkoho

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Eichfelder, G. (2020). Methods for Multiobjective Bilevel Optimization. In: Dempe, S., Zemkoho, A. (eds) Bilevel Optimization. Springer Optimization and Its Applications, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-52119-6_15

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