We consider the semi‐infinite optimization problem:
via a (by now standard) hierarchy of semidefinite relaxations, and for increasing values of d. In practice d is fixed, small, and one relaxes the constraint θd≤0 to θd(x)≤ϵ with ϵ>0, allowing us to change ϵ dynamically. As d increases, the limit of the optimal value is bounded above by f*+ϵ.