  We establish a geometric Pontryagin maximum principle for discrete time
optimal control problems on finite dimensional smooth manifolds under the
following three types of constraints: a) constraints on the states pointwise in
time, b) constraints on the control actions pointwise in time, c) constraints
on the frequency spectrum of the optimal control trajectories. Our proof
follows, in spirit, the path to establish geometric versions of the Pontryagin
maximum principle on smooth manifolds indicated in [Cha11] in the context of
continuous-time optimal control.
