Control-based Design and Analysis of Gradient-Tracking Algorithms for Distributed Quadratic Optimization

In this work we design an iterative distributed optimization algorithm, based on the well-known distributed gradient tracking algorithm. We show the advantages of a system theoretical approach on a distributed optimization framework in which the cost function is given by a sum of quadratic functions. In other words, the main idea of the work consists in seeing the update equation characterizing an iterative optimization algorithm as the dynamics equation of a discrete-time system in which the decision variable plays the state variable role. The goal of the work is to show how system and control theory tools can be used to force this state variable to the optimum of the considered cost function even in presence of disturbances and/or uncertainties. So, the design of a distributed optimization algorithm is seen as the design of a controller able to solve the set point control problem in which the reference signal is given by the optimum of the considered cost function.