Distributed zero-gradient-sum algorithm for convex optimization with time-varying communication delays and switching networks

The distributed convex optimization problem subject to time-varying communication delays and switching network topologies is addressed in this paper. Based on continuous-time Zero-Gradient-Sum scheme, the novel distributed algorithms are proposed to minimize the global objective function which is composed of a sum of strictly convex local cost functions. In the fixed network topology case, by constructing a new Lyapunov-Krasovskii function, two explicit sufficient conditions for the maximum admissible time delay are derived to guarantee that all agents' states converge to the optimal solution. In the switching network topology case, the stability condition is derived by the common Lyapunov function theory. In addition, two sufficient conditions about the maximum admissible time delays are also derived for the fixed and switching weight-balanced network topologies, respectively. Several simulation tests are used to illustrate the effectiveness of our obtained theoretical results.