Asynchronous Algorithm for Distributed Multi-agent Convex Optimization

This paper proposes an asynchronous algorithm for distributed optimization problem (Asy-DOP) in multi-agent network with gradient noise. The algorithm can be implemented in an asynchronous distributed way. The objective function of the algorithm is the sum of the local functions of multiple nodes in the network, each node only knows its own local objective function and can exchange information with its neighbors. In addition, the algorithm is based on the undirected connected graph and requires the objective function is Lipschitz continuous. The step-size of the proposed algorithm is homogeneous and when the step-size is in a suitable range, it is proved that the convergence rate of the proposed algorithm is $O\left( {1/\sqrt k } \right)$, where the k is the number of iterations.