Reference : Mixed-integer sets from two rows of two adjacent simplex bases
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
Mixed-integer sets from two rows of two adjacent simplex bases
Andersen, Kent [Otto-von-Guericke Universität Magdeburg > Institut für Mathematische Optimierung > > >]
Louveaux, Quentin mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Optimisation discrète >]
Weismantel, Robert [Otto-von-Guericke Universität Magdeburg > Institut für Mathematische Optimierung > > >]
Mathematical Programming
[en] Mixed-integer programming ; Two Rows ; Lattice-point-free polyhedra
[en] In 2007 we studied a mixed-integer set arising from two rows of a
simplex tableau. We showed that facets of such a set can be obtained from
lattice point free triangles and quadrilaterals associated with either three or
four variables. In this paper we generalize our findings and show that, when
upper bounds on the non-basic variables are also considered, further classes
of facets arise that cannot be obtained from triangles and quadrilaterals.
Specifically, when exactly one upper bound on a non-basic variable is intro-
duced, stronger inequalities that can be derived from pentagons involving up
to six variables also appear.

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