Finite‐Time Average Consensus Based Approach for Distributed Convex Optimization

Abstract

AbstractIn this paper, we consider a distributed convex optimization problem where the objective function is an average combination of individual objective function in multi‐agent systems. We propose a novel Newton Consensus method as a distributed algorithm to address the problem. This method utilises the efficient finite‐time average consensus method as an information fusion tool to construct the exact Newtonian global gradient direction. Under suitable assumptions, this strategy can be regarded as a distributed implementation of the classical standard Newton method and eventually has a quadratic convergence rate. The numerical simulation and comparison experiment show the superiority of the algorithm in convergence speed and performance.