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A special three-level optimization problem

Author

Listed:
  • S. Dempe

    (TU Bergakademie Freiberg)

  • O. Khamisov

    (Sobolev Institute of Mathematics)

  • Yu. Kochetov

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

Abstract

A special linear, three-level optimization problem is considered where the reaction of the third-level decision maker influences the objective functions of both decision makers on the first and the second level via its optimal objective function value. For this problem, existence of an optimal solution as well as its computation are investigated.

Suggested Citation

  • S. Dempe & O. Khamisov & Yu. Kochetov, 2020. "A special three-level optimization problem," Journal of Global Optimization, Springer, vol. 76(3), pages 519-531, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00822-w
    DOI: 10.1007/s10898-019-00822-w
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    References listed on IDEAS

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    1. Florensa, Carlos & Garcia-Herreros, Pablo & Misra, Pratik & Arslan, Erdem & Mehta, Sanjay & Grossmann, Ignacio E., 2017. "Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches," European Journal of Operational Research, Elsevier, vol. 262(2), pages 449-463.
    2. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    3. Alizadeh, S.M. & Marcotte, P. & Savard, G., 2013. "Two-stage stochastic bilevel programming over a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 92-105.
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