Develop a new rounding method for convex polytopes

The goal of this project is to improve currently existing implementations for rounding convex polytopes from Volesti as well as develop a new method and analyze its performance. The new method be using the available C++ implementation from Volesti of the Khachiyan algorithm for solving the minimum volume enclosing ellipsoid (MVEE), which will then be transformed into the maximum volume ellipsoid of the polytope (MVE). Finally, the polytope will be brought into John position using the transformation that maps the MVE to the unit ball. The performance of the improved implementations and the new one will then be compared to existing rounding procedures from PolyRound.