  We consider a class of multi-agent cooperative consensus optimization
problems with local nonlinear convex constraints where only those agents
connected by an edge can directly communicate, hence, the optimal consensus
decision lies in the intersection of these private sets. We develop an
asynchronous distributed accelerated primal-dual algorithm to solve the
considered problem. The proposed scheme is the first asynchronous method with
an optimal convergence guarantee for this class of problems, to the best of our
knowledge. In particular, we provide an optimal convergence rate of
$\mathcal{O(1/K)}$ for suboptimality, infeasibility, and consensus violation.
