Distributed convex optimization in networks of agents with single-integrator dynamics

Abstract

In this paper, distributed convex optimization problem over undirected dynamical networks is studied. Here, networked agents are supposed to rendezvous at a point that is the solution of a global convex optimization problem with some local inequality constraints. To this end, all agents shall cooperate with their neighbors to seek the optimum point of the network's global objective function. A consensus-based distributed optimization algorithm is proposed, which combines an interior-point optimization algorithm with a nonlinear consensus protocol to find the optimum value of a convex objective function. We tackle this problem by addressing its subproblems, namely a consensus problem and a convex optimization problem. Firstly, we propose a saturation protocol for the consensus subproblem. Then, to solve the distributed optimization part, we implement an updating rule, which yields the optimum value of the global objective function, with the help of local estimators in a distributed way. Convergence analysis for the proposed protocol based on the Lyapunov stability theory for time-varying nonlinear systems is included. A simulation example is given at the end to illustrate the effectiveness of the proposed algorithm.