Distributed Convex Optimization in Networks of Agents with Single Integrator Dynamics

In this paper, distributed convex optimization problem over non-directed dynamical networks is studied. Here, networked agents with single-integrator dynamics 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 networks global objective function. A distributed optimization algorithm based on the interior-point method is proposed, which combines an optimization algorithm with a nonlinear consensus protocol to find the optimum value of the global objective function. We tackle this problem by addressing its sub-problems, namely a consensus problem and a convex optimization problem. Firstly, we propose a saturation protocol for the consensus sub-problem. Then to solve the distributed optimization part, we implement a centralized control law, which yields the optimum value of the global objective function, in a distributed fashion with the help of a distributed estimator. Convergence analysis for the proposed protocol based on the 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.