  This article treats optimal sparse control problems with multiple constraints
defined at intermediate points of the time domain. For such problems with
intermediate constraints, we first establish a new Pontryagin maximum principle
that provides first order necessary conditions for optimality in such problems.
Then we announce and employ a new numerical algorithm to arrive at, in a
computationally tractable fashion, optimal state-action trajectories from the
necessary conditions given by our maximum principle. Several detailed
illustrative examples are included.
