Fully Distributed Continuous-Time Algorithm for Nonconvex Optimization Over Unbalanced Digraphs

Abstract

This paper studies the distributed continuous-time nonconvex optimization problem of multi-agent systems over unbalanced digraphs. Each agent is endowed with a local cost function, which is privately known to the agent but not necessarily convex. We aim to drive all the agents to cooperatively converge to the optimal solution of the sum of all local cost functions. Based on the adaptive control approach, a fully distributed algorithm is developed for each agent in the case that neither prior global information concerning network connectivity nor convexity of local cost functions is available. A key feature of the algorithm is that it removes the dependence on the smallest strong convexity constant of local cost functions, and the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix of unbalanced digraphs.