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Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

In: Bilevel Optimization

Author

Listed:
  • Stephan Dempe

    (Institute of Numerical Mathematics and Optimization)

Abstract

Bilevel optimization problems are hierarchical optimization problems where the feasible region of the so-called upper level problem is restricted by the graph of the solution set mapping of the lower level problem. Aim of this article is to collect a large number of references on this topic, to show the diversity of contributions and to support young colleagues who try to start research in this challenging and interesting field.

Suggested Citation

  • Stephan Dempe, 2020. "Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 581-672, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_20
    DOI: 10.1007/978-3-030-52119-6_20
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    Citations

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    Cited by:

    1. Julia Grübel & Richard Krug & Martin Schmidt & Winnifried Wollner, 2023. "A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1077-1117, September.
    2. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    3. Akshit Goyal & Yiling Zhang & Chuan He, 2023. "Decision Rule Approaches for Pessimistic Bilevel Linear Programs Under Moment Ambiguity with Facility Location Applications," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1342-1360, November.
    4. Li, Na & Okur, Özge, 2023. "Economic analysis of energy communities: Investment options and cost allocation," Applied Energy, Elsevier, vol. 336(C).
    5. Elisabetta Allevi & Didier Aussel & Rossana Riccardi & Domenico Scopelliti, 2024. "Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 344-370, January.
    6. R. Cambini & R. Riccardi & D. Scopelliti, 2023. "Solving linear multiplicative programs via branch-and-bound: a computational experience," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    7. G. Constante-Flores & A. J. Conejo & S. Constante-Flores, 2022. "Solving certain complementarity problems in power markets via convex programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 465-491, October.
    8. Maximilian Merkert & Galina Orlinskaya & Dieter Weninger, 2022. "An exact projection-based algorithm for bilevel mixed-integer problems with nonlinearities," Journal of Global Optimization, Springer, vol. 84(3), pages 607-650, November.
    9. Daniel Villamar & Didier Aussel, 2024. "A bilevel optimization approach of energy transition in freight transport: SOS1 method and application to the Ecuadorian case," Computational Management Science, Springer, vol. 21(2), pages 1-30, December.

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