  We present an Alternating Direction Method of Multipliers (ADMM) algorithm
for solving optimization problems with an l_1 regularized least-squares cost
function subject to recursive equality constraints. The considered optimization
problem has applications in control, for example in l_1 regularized MPC. The
ADMM algorithm is easy to implement, converges fast to a solution of moderate
accuracy, and enables separation of the optimization problem into sub-problems
that may be solved in parallel. We show that the most costly step of the
proposed ADMM algorithm is equivalent to solving an LQ regulator problem with
an extra linear term in the cost function, a problem that can be solved
efficiently using a Riccati recursion. We apply the ADMM algorithm to an
example of l_1 regularized MPC. The numerical examples confirm fast convergence
to moderate accuracy and a linear complexity in the MPC prediction horizon.
