  Recently, distributed dual averaging has received increasing attention due to
its superiority in handling constraints and dynamic networks in multiagent
optimization. However, all distributed dual averaging methods reported so far
considered nonsmooth problems and have a convergence rate of
$O(\frac{1}{\sqrt{t}})$. To achieve an improved convergence guarantee for
smooth problems, this work proposes a second-order consensus scheme that
assists each agent to locally track the global dual variable more accurately.
This new scheme in conjunction with smoothness of the objective ensures that
the accumulation of consensus error over time caused by incomplete global
information is bounded from above. Then, a rigorous investigation of dual
averaging with inexact gradient oracles is carried out to compensate the
consensus error and achieve an $O(\frac{1}{t})$ convergence rate. The proposed
method is examined in a large-scale LASSO problem.
