Abstract:The design of distributed discrete-time algorithms to cooperatively solve an additive cost optimization problem in multi-agent networks is presented in this paper.The striking feature of the distributed algorithms lies in the use of only the sign of the relative state information between neighbors;which substantially differentiates our algorithms from the existing ones.Moreover,the algorithm does not require the interaction matrix to be doubly stochastic.We first interpret the proposed algorithms in terms of the penalty method in the optimization theory and then perform a non-asymptotic analysis to study the convergence for static network graphs.Compared with the celebrated distributed subgradient algorithms,which,however,use the exact relative state information,the convergence speed in the proposed algorithms is essentially not affected by the loss of information.We also extend our results to the cases of deterministically and randomly time-varying graphs.Finally,we validate the theoretical results through simulations.