A discontinuous algorithm for distributed convex optimization

In this paper we present a novel discontinuous algorithm which cooperatively solves a distributed convex multi-agent optimization problem under a consensus constraint. The team performance function is the sum of local quadratic objective functions which are known to the local agent only. The proposed local interaction rule between the agents employs the subgradient of the local objective function along with a PI-like discontinuous component enforcing consensus between the agents' states in finite-time. Under mild assumptions on the local cost, a formal Lyapunov analysis confirms the convergence properties of the algorithm towards the optimal solution of the considered problem. To corroborate the theoretical results simulative analysis are presented