Distributed online aggregation optimization with time‐varying constraints

Abstract This paper mainly studies the distributed online optimization problem with aggregation variables and time‐varying convex constraints. All agents collaborate to minimize the sum of local convex functions, where each local cost function is just accessed by one agent and has two variables, including the decision of the agent and aggregation variable of all agents decisions. Different from the most existing works, where the constraint sets were assumed to be time‐invariable, this paper considers the situation of time‐varying constraints by introducing the one‐way Hausdorff distance. First, a new projected aggregation tracking algorithm is proposed, which can guarantee that the decisions of all agents stay at the time‐varying constraints all the time. Second, it is proved that the dynamic regret has a sublinear upper bound. Finally, numerical experiments are conducted to validate the effectiveness of the proposed algorithm.