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We study a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A new decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The iterative algorithm is implemented on a multi-hop network and is designed to handle communication delays. The convergence of the algorithm is proved for communication networks with bounded delays. An explicit bound, which depends on the communication delays, on the convergence rate is given. A numerical comparison with a decentralized primal algorithm shows that the dual algorithm converges faster, with less communication.