Methods for Multiobjective Bilevel Optimization

Gabriele Eichfelder ()
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Gabriele Eichfelder: TU Ilmenau

Chapter Chapter 15 in Bilevel Optimization, 2020, pp 423-449 from Springer

Abstract: 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.

Keywords: Multiobjective bilevel optimization; Semivectorial bilevel problem; Scalarization; Optimistic approach; Numerical methods (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-52119-6_15

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DOI: 10.1007/978-3-030-52119-6_15

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