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The convex hull of the all-different system with the inclusion property: a simple proof

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  • DI SUMMA, Marco

    (Dipartimento di Matematica, Università degli Studi di Padova, Italy)

Abstract

An all-different constraint for a given family of discrete variables imposes the condition that no two variables in the family are allowed to take the same value. Magos et al. [Mathematical Programming, 132 (2012), pp. 209–260] gave a linear-inequality description of the convex hull of solutions to a system of all-different constraints, under a special assumption called inclusion property. The convex hull of solutions is in this case the intersection of the convex hulls of each of the all-different constraints of the system. We give a short and simple proof of this result, that in addition shows the total dual integrality of the linear system.

Suggested Citation

  • DI SUMMA, Marco, 2013. "The convex hull of the all-different system with the inclusion property: a simple proof," LIDAM Discussion Papers CORE 2013069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2013069
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    Cited by:

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    4. NESTEROV, Yu. & SHIKHMAN, Vladimir, 2014. "Convergent subgradient methods for nonsmooth convex minimization," LIDAM Discussion Papers CORE 2014005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    all-different constraint; convex hull; integral polyhedron; total dual integrality;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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