  The present paper considers leveraging network topology information to
improve the convergence rate of ADMM for decentralized optimization, where
networked nodes work collaboratively to minimize the objective. Such problems
can be solved efficiently using ADMM via decomposing the objective into easier
subproblems. Properly exploiting network topology can significantly improve the
algorithm performance. Hybrid ADMM explores the direction of exploiting node
information by taking into account node centrality but fails to utilize edge
information. This paper fills the gap by incorporating both node and edge
information and provides a novel convergence rate bound for decentralized ADMM
that explicitly depends on network topology. Such a novel bound is attainable
for certain class of problems, thus tight. The explicit dependence further
suggests possible directions to optimal design of edge weights to achieve the
best performance. Numerical experiments show that simple heuristic methods
could achieve better performance, and also exhibits robustness to topology
changes.
