Distributed Online Projection Tracking for Constrained Aggregative Optimization Under Directed Graph

In this paper, we consider an online constrained aggregative optimization problem over directed communication topology. Specially, for each agent, the local cost function is determined by a local set constraint, a local decision variable, and an aggregative function of all agents' decision variable; the local set constraints, the global/local cost functions, and the aggregative function are all time varying. In order to address such setting, we develop an online distributed projected aggregative optimization algorithm. We show that the mean dynamic regret is converged to a bound constant under directed communication graph. Thus, our proposed online projected aggregative optimization method can not only deal with a class of general optimization problems, but also can be applied to the general directed networks. Some theoretical analyses and numerical simulations are conducted to verify the effectiveness of the proposed algorithm.