Distributed constrained optimization for multi-agent networks with communication delays under time-varying topologies

In this paper, a distributed constrained optimization problem for discrete -time multi -agent systems with timevarying directed graphs is studied and a distributed projection subgradient algorithm is proposed. Furthermore, we investigate the scenario involving time delays in agent interactions and use an augmented matrix method to deal with delays. Specifically, we introduce virtual nodes along with delay edges to effectively transform the system with delays into an equivalent augmented system. It is shown that for our considered systems the agents' estimates obtained by this algorithm converge to the same optimal solution. Finally, simulations examples are given to verify the effectiveness of the proposed algorithm.