A gradient tracking method for resource allocation base on distributed convex optimization

In this paper we consider the distributed resource allocation problem, where the individual cost of each agent attempts to minimize when both the total resource and the capacity of local agents are limit. This problem is encountered in many practical applications such as demand response, cloud computing systems and economic dispatch of power systems. This kind of problem can be expressed as an optimization problem under constraints. Our goal is to obtain the optimal resource allocation under limited conditions and the global objective function is a sum of all local agents individual cost function. By combining with the distributed primal-dual method, we design a distributed optimization algorithm with a constant step-size. When the cost function of each agent is convex and smooth, we prove that our method can converge to the optimal solution. Finally, we apply the algorithm to the problem of the economic dispatch in power systems and get the optimal resource allocation, which verifies the effectiveness of the algorithm.