We consider the quantum control of molecular dynamics in the strong response regime. The method used is based on a formulation in Liouville space and is valid for both the weak and strong response regimes. Several previous examples using this formulation in the weak response regime have shown that it is possible to overcome the natural tendency of wave packets to delocalize as they evolve on Bom-Oppenheimer potential surfaces. In this work we demonstrate that the weak field solutions for the optimal electric field can be surprisingly robust, in the sense that, by increasing their intensity without altering their form, they can be extended well beyond the first-order, perturbative limit to the regime in which significant population transfer occurs, while retaining a high deg-ree of control. Further, since the weak field solutions are robust with respect to field strength, they can be used as initial guesses in a procedure to find locally optimal strong response solutions using an iterative search scheme. As a numerical application of the theory, we demonstrate the control of the vibrational dynamics of nuclear wave packets on an electronically excited state of I-2.