  This paper introduces an efficient first-order method based on the
alternating direction method of multipliers (ADMM) to solve semidefinite
programs (SDPs) arising from sum-of-squares (SOS) programming. We exploit the
sparsity of the \emph{coefficient matching conditions} when SOS programs are
formulated in the usual monomial basis to reduce the computational cost of the
ADMM algorithm. Each iteration of our algorithm requires one projection onto
the positive semidefinite cone and the solution of multiple quadratic programs
with closed-form solutions free of any matrix inversion. Our techniques are
implemented in the open-source MATLAB solver SOSADMM. Numerical experiments on
SOS problems arising from unconstrained polynomial minimization and from
Lyapunov stability analysis for polynomial systems show speed-ups compared to
the interior-point solver SeDuMi, and the first-order solver CDCS.
