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Methods for Multiobjective Bilevel Optimization

In: Bilevel Optimization

Author

Listed:
  • Gabriele Eichfelder

    (TU Ilmenau)

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.

Suggested Citation

  • Gabriele Eichfelder, 2020. "Methods for Multiobjective Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 423-449, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_15
    DOI: 10.1007/978-3-030-52119-6_15
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