hypersimplex for special cases
Posted: 30 Aug 2012, 09:28
Is there a specific reason why hypersimplex(0,d) and hypersimplex(d,d) are not allowed? Of course the resulting polytopes are just single points but I really "needed" them:
For example, one can describe the even-parity polytope (convex hull of 0/1 points with even number of 1's) by a disjunctive-programming construction (convex hull of union of polyhedra) of all k-hypersimplices for which k is an even integer. Using my extension for extended formulations this works as follows for the odd case:(here $Q is the extended formulation and you obtain the odd-parity polytope if you apply the projection via matrix $Proj)
Since I want to be able to do the same thing for the even case, I need hypersimplex(0,6), etc...
Best regards,
Matthias
For example, one can describe the even-parity polytope (convex hull of 0/1 points with even number of 1's) by a disjunctive-programming construction (convex hull of union of polyhedra) of all k-hypersimplices for which k is an even integer. Using my extension for extended formulations this works as follows for the odd case:
Code: Select all
($Q,$Proj) = construct_disjunctive_program(hypersimplex(1,6), hypersimplex(3,6), hypersimplex(5,6));Since I want to be able to do the same thing for the even case, I need hypersimplex(0,6), etc...
Best regards,
Matthias
