Possibilities are discussed for global optimization of quantum wells based on ternary alloys, with respect to third-order intersubband susceptibilities at resonance. The method employed in this work relies on variational calculus, i.e. optimal control theory, combined with the simulated annealing method in the initial phase of optimization. Its use is demonstrated by designing AlxGa1−xAs quantum wells intended for resonant third harmonic generation with pump photon energy, the objective being the largest susceptibility achievable with the chosen material system.