We study the equilibrium and nonequilibrium properties of strongly interacting bosons on a lattice in the presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose-Hubbard model and obtain the Mott insulator, Bose glass, and superfluid phases. We also study the nonequilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter, and the energy pumped into the system in this process as a function of the inverse ramp rate tau. For the clean case the density of excitations goes to a constant, while the order parameter and energy relax as 1/tau and 1/tau(2) respectively. With disorder, the excitation density decays exponentially with t, with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as tau is increased. DOI: 10.1103/PhysRevB.86.214207