I want to find the biggest axis parallel cuboid in an ellipsoid which may not be parallel to the axis.
The ellipsoid satisfies: $(X-X_0)^T\ A\ (X-X_0) + c < 0$,
where $X_0$ is the center of the ellipsoid. $A$ is the weighting matrix decides the shape and orientation of the ellipsoid. $c$ is a constant number.
Any help is appreciated!