On Khachiyan’s Algorithm for the Computation of Minimum Volume Enclosing Ellipsoids

Given $\cA := \{a^1,\ldots,a^m\} \subset \R^d$ whose affine hull is $\R^d$, we study the problems of computing an approximate rounding of the convex hull of $\cA$ and an approximation to the minimum volume enclosing ellipsoid of $\cA$. In the case of centrally symmetric sets, we first establish that Khachiyan’s barycentric coordinate descent (BCD) method is … Read more