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Geometric Algorithm for Multiparametric Linear Programming

Author

Listed:
  • F. Borrelli

    (Swiss Federal Institute of Technology, ETH)

  • A. Bemporad

    (Universita di Siena)

  • M. Morari

    (Swiss Federal Institute of Technology, ETH)

Abstract

We propose a novel algorithm for solving multiparametric linear programming problems. Rather than visiting different bases of the associated LP tableau, we follow a geometric approach based on the direct exploration of the parameter space. The resulting algorithm has computational advantages, namely the simplicity of its implementation in a recursive form and an efficient handling of primal and dual degeneracy. Illustrative examples describe the approach throughout the paper. The algorithm is used to solve finite-time constrained optimal control problems for discrete-time linear dynamical systems.

Suggested Citation

  • F. Borrelli & A. Bemporad & M. Morari, 2003. "Geometric Algorithm for Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 515-540, September.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:3:d:10.1023_b:jota.0000004869.66331.5c
    DOI: 10.1023/B:JOTA.0000004869.66331.5c
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    References listed on IDEAS

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    1. Vivek Dua & Efstratios Pistikopoulos, 2000. "An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems," Annals of Operations Research, Springer, vol. 99(1), pages 123-139, December.
    2. Tomas Gal & Josef Nedoma, 1972. "Multiparametric Linear Programming," Management Science, INFORMS, vol. 18(7), pages 406-422, March.
    3. GAL, Thomas & NEDOMA, Jozef, 1972. "Multiparametric linear programming," LIDAM Reprints CORE 115, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Richard Oberdieck & Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2014. "A branch and bound method for the solution of multiparametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 59(2), pages 527-543, July.
    3. Chen, Yue & Wei, Wei & Liu, Feng & Mei, Shengwei, 2016. "Distributionally robust hydro-thermal-wind economic dispatch," Applied Energy, Elsevier, vol. 173(C), pages 511-519.
    4. C. Filippi, 2004. "An Algorithm for Approximate Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 73-95, January.
    5. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    6. J. Spjøtvold & P. Tøndel & T. A. Johansen, 2007. "Continuous Selection and Unique Polyhedral Representation of Solutions to Convex Parametric Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 177-189, August.
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    11. Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2013. "On the global solution of multi-parametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 57(1), pages 51-73, September.
    12. Hladík, Milan, 2010. "Multiparametric linear programming: Support set and optimal partition invariancy," European Journal of Operational Research, Elsevier, vol. 202(1), pages 25-31, April.

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