Finite‐time convergent distributed consensus optimisation over networks

In this study, a finite‐time convergent distributed continuous‐time algorithm is proposed to solve a network optimisation problem where the global cost function is the sum of strictly convex local cost functions under an undirected network with fixed topologies. The algorithm is inspired by finite‐time consensus protocols and continuous‐time zero‐gradient‐sum algorithms. Instead of the exponential convergence in existing works, the finite‐time convergence is guaranteed based on the Lyapunov method. A numerical simulation example is provided to illustrate the effectiveness of the developed algorithm.