  This paper considers a convex optimization problem with cost and constraints
that evolve over time. The function to be minimized is strongly convex and
possibly non-differentiable, and variables are coupled through linear
constraints. In this setting, the paper proposes an online algorithm based on
the alternating direction method of multipliers (ADMM), to track the optimal
solution trajectory of the time-varying problem; in particular, the proposed
algorithm consists of a primal proximal gradient descent step and an
appropriately perturbed dual ascent step. The paper derives tracking results,
asymptotic bounds, and linear convergence results. The proposed algorithm is
then specialized to a multi-area power grid optimization problem, and our
numerical results verify the desired properties.
