Continuous knapsack sets with divisible capacities
We study two continuous knapsack sets Y≥ and Y≤ with n integer, one unbounded continuous and m bounded continuous variables in either ≥ or ≤ form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and 2m polyhedra arising from a continuous knapsack set with a single unbounded continuous variable. The latter polyhedra are in turn completely described by an exponential family of partition inequalities. A polynomial size extended formulation is known in the ≥ case. We provide an extended formulation for the ≤ case. It follows that, given a specific objective function, optimization over both Y≥ and Y≤ can be carried out by solving a polynomial size linear program. A consequence of these results is that the coefficients of the continuous variables all take the values 0 or 1 (after scaling) in any non-trivial facet-defining inequality.
|Date of creation:||11 Dec 2013|
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- GAUTIER, Axel & POUDOU, Jean-Christophe, 2013.
"Reforming the postal universal service,"
CORE Discussion Papers
2013024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Nigar Hashimzade & Jean Hindriks & Gareth D. Myles, 2006. "Solutions Manual to Accompany Intermediate Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582694, June.
- Förster, Manuel & Mauleon, Ana & Vannetelbosch, Vincent J., 2016.
"Trust and manipulation in social networks,"
Cambridge University Press, vol. 4(02), pages 216-243, June.
- Manuel Förster & Ana Mauleon & Vincent Vannetelbosch, 2013. "Trust and Manipulation in Social Networks," Documents de travail du Centre d'Economie de la Sorbonne 13065, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- FORSTER, Manuel & MAULEON, Ana & VANNETELBOSCH, Vincent, 2013. "Trust and manipulation in social networks," CORE Discussion Papers 2013050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Manuel Förster & Ana Mauleon & Vincent Vannetelbosch, 2013. "Trust and Manipulation in Social Networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00881145, HAL.
- Manuel Förster & Ana Mauleon & Vincent J. Vannetelbosch, 2014. "Trust and Manipulation in Social Networks," Working Papers 2014.50, Fondazione Eni Enrico Mattei.
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