Online optimization has emerged as powerful tool in large scale optimization. In
this paper, we introduce efficient online algorithms based on the alternating
directions method (ADM). We introduce a new proof technique for ADM in the batch
setting, which yields a $O(1/T)$ convergence rate for ADM and forms the basis of
regret analysis in the online setting. We consider two scenarios in the online
setting, based on whether the solution needs to lie in the feasible set in every
iteration or not. In both settings, we establish regret bounds for both the
objective function as well as constraint violation for general and strongly
convex functions. Preliminary results are presented to illustrate
the performance of the proposed algorithms.