A new algorithm to solve numerically the evolution of empirical shell models of polarizable systems is presented. It employs constrained molecular dynamics to satisfy exactly, at each time step, the crucial condition that the gradient of the potential with respect to the shell degrees of freedom is null. The algorithm is efficient, stable, and, contrary to the available alternatives, it is symplectic and time reversible. A proof-of-principle calculation on a polarizable model for NaCl is presented to illustrate its properties in comparison with the current method, which employs a conjugate-gradient procedure to enforce the null gradient condition. The proposed algorithm is applicable to other cases where a minimum condition on a function of an auxiliary set of driven dynamical variables must be satisfied.