  In this paper, we propose a fully distributed algorithm for second-order
continuous-time multi-agent systems to solve the distributed optimization
problem. The global objective function is a sum of private cost functions
associated with the individual agents and the interaction between agents is
described by a weighted undirected graph. We show the exponential convergence
of the proposed algorithm if the underlying graph is connected, each private
cost function is locally gradient-Lipschitz-continuous, and the global
objective function is restricted strongly convex with respect to the global
minimizer. Moreover, to reduce the overall need of communication, we then
propose a dynamic event-triggered communication mechanism that is free of Zeno
behavior. It is shown that the exponential convergence is achieved if the
private cost functions are also globally gradient-Lipschitz-continuous.
Numerical simulations are provided to illustrate the effectiveness of the
theoretical results.
