  We address the solution of time-varying optimization problems characterized
by the sum of a time-varying strongly convex function and a time-invariant
nonsmooth convex function. We design an online algorithmic framework based on
prediction-correction, which employs splitting methods to solve the sampled
instances of the time-varying problem. We describe the prediction-correction
scheme and two splitting methods, the forward-backward and the
Douglas-Rachford. Then by using a result for generalized equations, we prove
convergence of the generated sequence of approximate optimizers to a
neighborhood of the optimal solution trajectory. Simulation results for a
leader following formation in robotics assess the performance of the proposed
algorithm.
