Unconstrained Minimization
At the -th iteration of the algorithm, we have a point at the center of an ellipsoid . We query the cutting-plane oracle to obtain a vector such that . We therefore conclude that
We set to be the ellipsoid of minimal volume containing the half-ellipsoid described above and compute . The update is given by
where . The stopping criterion is given by the property that
Read more about this topic: Ellipsoid Method