Finite-Time Average Consensus Based Approach for Distributed Convex Optimization

In 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.