* If the approximate oracle returns a solution with value larger than 1, then <math>\mathbf{y}_t</math> is definitely infeasible, and the solution correspond to a configuration that violates a constraint '''a'''. We do a "feasibility cut", cutting the ellipsoid all points '''y''' for which <math>\mathbf{a}\cdot \mathbf{y} > 1</math>.
* If the approximate oracle returns a solution with value at most 1, then '''<math>\mathbf{y}_t</math>''' may or may not be feasible. However, we still considerdo itan a"optimality cut": we cut from the ellipsoid all points '''y''' for which <math>\mathbf{n}\cdot \mathbf{y} < \mathbf{n}\cdot \mathbf{y}_t</math>. {{Clarify|date=January 2022}}
* If the approximate oracle says that <math>\mathbf{y}_t</math> is feasible, then we do an "optimality cut": we cut from the ellipsoid all points '''y''' for which <math>\mathbf{n}\cdot \mathbf{y} < \mathbf{n}\cdot \mathbf{y}_t</math>. These points are definitely not optimal.
*
After making a cut, we construct a new, smaller ellipsoid. It can be shown that this process converges to an approximate solution, in time polynomial in the required accuracy.
* If the approximate oracle returns a solution with value larger than 1, then '''y''' is definitely infeasible, and the solution correspond to a configuration that violates a constraint.
