Minimum Area Enclosing Ellipsoidal Cylinder Problem

Given an arbitrary set A ∈ IRn, we know that there exists an ellipsoid E which provides an n-rounding of the set A, i.e. n−1E ⊆ conv(A) ⊆ E. The minimum-volume ellipsoid that encloses the set A provides such an ellipsoid and will be denoted as MVEE(A). Finding good approximations to this ellipsoid is very useful for many applications in computational geometry, com-putational statistics, and convex optimization. For example, given a 2-D (or 3-D) image of a convex ob-ject, the area (or the volume) of the minimum-volume enclosing ellipsoid provides a good approximation to the actual area (or the volume) of the object and can be useful in image processing applications. The problem of finding the minimum-volume enclos-ing ellipsoid for a given set, referred to as the MVE