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Bilevel Programming: A Combinatorial Perspective

In: Graph Theory and Combinatorial Optimization

Author

Listed:
  • Patrice Marcotte
  • Gilles Savard

Abstract

Bilevel programming is a branch of optimization where a subset of variables is constrained to lie in the optimal set of an auxiliary mathematical prograri. This chapter presents an overview of two specific classes cf bilevel programs, and in particular their relationship to well-known combinatorial problems.

Suggested Citation

  • Patrice Marcotte & Gilles Savard, 2005. "Bilevel Programming: A Combinatorial Perspective," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 191-217, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25592-7_7
    DOI: 10.1007/0-387-25592-3_7
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    Citations

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    Cited by:

    1. Biermann, Florian M. & Naroditskiy, Victor & Polukarov, Maria & Nguyen, Tri-Dung & Rogers, Alex & Jennings, Nicholas R., 2014. "Task assignment with controlled and autonomous agents," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 116-121.
    2. Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.
    3. Qiu, Xuan & Huang, George Q., 2016. "Transportation service sharing and replenishment/delivery scheduling in Supply Hub in Industrial Park (SHIP)," International Journal of Production Economics, Elsevier, vol. 175(C), pages 109-120.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. Jean Etoa, 2010. "Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 615-637, August.

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