A procedure is proposed for finding the globally optimal semiconductor quantum well profile in respect to the second order intersubband susceptibilities at resonance. It relies on the combined use of simulated annealing and variational calculus (i.e. the optimal control theory), and effectively performs a free variation of the quantum well (QW) profile, searching for the global optimum. The proposed method does not depend on the choice of input ("seed") potential and includes the variation of a continuous function instead of a set of scalar parameters, so it should lead to the globally optimal QW profile for a particular application, unconstrained to any particular class of functional forms.