  This paper studies optimization problems over multi-agent systems, in which
all agents cooperatively minimize a global objective function expressed as a
sum of local cost functions. Each agent in the systems uses only local
computation and communication in the overall process without leaking their
private information. Based on the Barzilai-Borwein (BB) method and
multi-consensus inner loops, a distributed algorithm with the availability of
larger stepsizes and accelerated convergence, namely ADBB, is proposed.
Moreover, owing to employing only row-stochastic weight matrices, ADBB can
resolve the optimization problems over unbalanced directed networks without
requiring the knowledge of neighbors' out-degree for each agent. Via
establishing contraction relationships between the consensus error, the
optimality gap, and the gradient tracking error, ADBB is theoretically proved
to converge linearly to the globally optimal solution. A real-world data set is
used in simulations to validate the correctness of the theoretical analysis.
