Finding a convex decomposition of a point in a polytope

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JQX
Posts: 5
Joined: 03 Nov 2014, 06:43

Finding a convex decomposition of a point in a polytope

Postby JQX » 20 Jun 2016, 20:44

A simple question: If v is a point in a polytope P, I would like to find an explicit convex combination of the vertices of P which equals v. Additionally suppose that we want to find an optimal decomposition into d+1 points, where d is the dimension of P.

Are there functions in polymake that do these things?

Thanks!

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joswig
Main Author
Posts: 280
Joined: 24 Dec 2010, 11:10

Re: Finding a convex decomposition of a point in a polytope

Postby joswig » 23 Jun 2016, 16:10

That can be solved in terms of a linear program. And, yes, via its many interfaces polymake can solve linear programs.


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