If what I assume is correct,
assumption : for a maximization problem, we run a binary search over estimated values, starting with max estimated value, and narrow down to the feasible optimal value with help of ellipsoid method. The ellipsoid method helps us to check for the feasibility of every proposed optimal value.
So we have to find whether a solution lies inside the convex set K of possible solutions. How does the particular initial ellipsoid chosen as an input for the algorithm reflect this solution whose feasibility we have to find out?