Continuous-Time Coordination Algorithm for Distributed Convex Optimization Over Weight-Unbalanced Directed Networks

Abstract

A distributed convex optimization problem over a weight-unbalanced directed network is studied in this brief, where the global objective function is equal to the sum of strongly convex objective functions with globally Lipschitz gradients. With respect to the optimization problem, a new continuous-time coordination algorithm is proposed to compute its optimal solution in a distributed manner. The asymptotical convergence of the proposed algorithm is guaranteed by resorting to the direct sum decomposition technique, Kronecker matrix algebra, the stability of perturbed systems, and input-to-state stability. Finally, some simulations are performed to illustrate the theoretical result.