Distributed optimal resource allocation over networked systems and use of an e-exact penalty function*

We consider an optimal resource allocation problem over networked systems with connected graph communication topologies. The global cost function in this problem is the sum of local convex cost functions of the agents and the constraints are the affine demand equation and local box constraints on the decision variable of each agent. To solve this problem, we propose a novel distributed continuous-time algorithm. Our solution takes advantage of a smooth e-exact penalty function method to handle the local box inequality constrains. In this paper, we also obtain a lower bound on the admissible values of the weight of our penalty function in terms of the size of the gradient of local cost functions. Then, we discuss how agents can use this lower bound to determine the penalty function weight in a distributed manner. Simulations illustrate our results.