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In this paper, we study the distributed optimization problem usingapproximate first-order information. We suppose the agent can repeatedly callan inexact first-order oracle of each individual objective function andexchange information with its time-varying neighbors. We revisit thedistributed subgradient method in this circumstance and show its suboptimalityunder square summable but not summable step sizes. We also present severalconditions on the inexactness of the local oracles to ensure an exactconvergence of the iterative sequences towards the global optimal solution. Anumerical example is given to verify the efficiency of our algorithm.

Distributed Optimization with Inexact Oracle