Distributed constrained optimization over unbalanced graphs and delayed gradient

Abstract

In this paper, we investigate a distributed constrained optimization problem subject to convex, closed, and nonidentical set constraints over unbalanced graphs, where each agent has local access to its strongly convex objective function and collaborates, minimizing the sum of these functions. To address this problem, we design a distributed projected delayed gradient algorithm by using the available delayed gradient information, which removes dependence on the current gradient information and increases iteration efficiency. Moreover, to improve communication robustness, the algorithm is only based on a row stochastic weight matrix and achieves an $O(1/T)$ convergence rate for a non-negative and diminishing step size. Finally, we present a numerical example to verify the effectiveness of the algorithm.