Distributed Subgradient Algorithm for Multi-agent Optimization with Uncoordinated Dynamic Stepsizes

We develop and analyze the distributed subgradient algorithm with uncoordinated dynamic stepsizes for multi-agent convex optimization problems. The proposed algorithm allows each agent i to utilize the time-varying estimate of the local function value at the global optimal solution to obtain its dynamically chosen stepsize. Theoretical analysis shows that the proposed algorithm leads all agents to reach a consensus on the optimal solution to the optimization problem. Moreover, the dynamic stepsizes can overcome inefficient calculations caused by the diminishing stepsizes in the existing distributed subgradient methods. Besides, numerical results are provided to illustrate the competitive performance of the proposed algorithm.