The Barzilai–Borwein Method for distributed optimization over unbalanced directed networks

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