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On the global solution of multi-parametric mixed integer linear programming problems

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  • Martina Wittmann-Hohlbein
  • Efstratios Pistikopoulos

Abstract

This paper deals with the global solution of the general multi-parametric mixed integer linear programming problem with uncertainty in the entries of the constraint matrix, the right-hand side vector, and in the coefficients of the objective function. To derive the piecewise affine globally optimal solution, the steps of a multi-parametric branch-and-bound procedure are outlined, where McCormick-type relaxations of bilinear terms are employed to construct suitable multi-parametric under- and overestimating problems. The alternative of embedding novel piecewise affine relaxations of bilinear terms in the proposed algorithmic procedure is also discussed. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:1:p:51-73
    DOI: 10.1007/s10898-012-9895-2
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    References listed on IDEAS

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    1. 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.
    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).
    4. Tomas Gal, 1975. "Rim Multiparametric Linear Programming," Management Science, INFORMS, vol. 21(5), pages 567-575, January.
    5. C. Filippi, 2004. "An Algorithm for Approximate Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 73-95, January.
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    Cited by:

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    3. Pubudu L. W. Jayasekara & Andrew C. Pangia & Margaret M. Wiecek, 2023. "On solving parametric multiobjective quadratic programs with parameters in general locations," Annals of Operations Research, Springer, vol. 320(1), pages 123-172, January.

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