An extension of disjunctive programming and its impact for compact tree formulations
In the 1970’s, Balas [2, 4] introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one can easily derive an extended formulation of the convex hull of the union of these polyhedra. In this paper, we give a generalization of this result by extending the polyhedral structure of the variables coupling the polyhedra taken in the union. Using this generalized concept, we derive polynomial size linear programming formulations (compact formulations) of a well- known spanning tree approximation of Steiner trees and flow equivalent trees for node- as well as edge- capacitated undirected networks. We also present a compact formulation for Gomory-Hu trees, and, as a consequence, of the minimum T-cut problem (but not for the associated T-cut polyhedron). Recently, Kaibel and Loos  introduced a more involved framework called polyhedral branching systems to derive extended formulations. The most of our model can be expressed in terms of their framework. The value of our model can be seen in the fact that it completes their framework with an interesting algorithmic aspect.
|Date of creation:||01 Jul 2010|
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- AMIR, Rabah, 2003.
"Supermodularity and complementarity in economics: an elementary survey,"
CORE Discussion Papers
2003104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
- AMIR, Rabah, "undated". "Supermodularity and complementarity in economics: an elementary survey," CORE Discussion Papers RP 1823, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
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