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This paper studies optimization problems over multi-agent systems, in whichall agents cooperatively minimize a global objective function expressed as asum of local cost functions. Each agent in the systems uses only localcomputation and communication in the overall process without leaking theirprivate information. Based on the Barzilai-Borwein (BB) method andmulti-consensus inner loops, a distributed algorithm with the availability oflarger stepsizes and accelerated convergence, namely ADBB, is proposed.Moreover, owing to employing only row-stochastic weight matrices, ADBB canresolve the optimization problems over unbalanced directed networks withoutrequiring the knowledge of neighbors' out-degree for each agent. Viaestablishing contraction relationships between the consensus error, theoptimality gap, and the gradient tracking error, ADBB is theoretically provedto converge linearly to the globally optimal solution. A real-world data set isused in simulations to validate the correctness of the theoretical analysis.

The Barzilai-Borwein Method for Distributed Optimization over Unbalanced Directed Networks