Distributed Mirror Descent With Integral Feedback: Asymptotic Convergence Analysis of Continuous-Time Dynamics

This letter addresses distributed optimization, where a network of agents wants to minimize global strongly convex objective function. The function can be written as sum local functions, each which is associated with an agent. We propose continuous-time mirror descent algorithm that uses purely information converge the optimum. Unlike previous work on descent, we incorporate integral feedback in update, allowing constant step-size when discretized. establish asymptotic convergence using Lyapunov stability analysis. further illustrate numerical experiments verify advantage adopting for improving rate descent.