The convergence rate of Newton-Raphson consensus optimization for quadratic cost functions

摘要: We consider the convergence rates of two convex optimization strategies in context multi agent systems, namely Newton-Raphson consensus and a distributed Gradient-Descent opportunely derived from first. To allow analytical derivations, analyses are performed under simplificative assumption quadratic local cost functions. In this framework we derive sufficient conditions which guarantee algorithms. From these then obtain closed form expressions that can be used to tune parameters for maximizing rate convergence. Despite formulae have been functions assumptions, they as rules-of-thumb tuning algorithms general situations.