Towards a Practical Volumetric Cutting Plane Method for Convex Programming
Kurt M. Anstreicher
We consider the volumetric cutting plane method for finding a
point in a convex set $\Ccal\subset\Re^n$ that is characterized by a
separation oracle. We prove polynomiality of the algorithm with
each added cut placed directly through the current point, and show that
this ``central cut" version of the method can be implemented using no
more than $25n$ constraints at any time.