We propose a new algorithm for approximate MAP inference on factor graphs, by combining augmented Lagrangian optimization with the dual decomposition method. Each slave subproblem is given a quadratic penalty, which pushes toward faster consensus than in previous subgradient approaches. Our algorithm is provably convergent, parallelizable, and suitable for fine decompositions of the
graph. We show how it can efficiently handle problems with (possibly global) structural constraints via simple sort operations. Experiments on synthetic and real-world data show that our approach compares favorably with the state-of-the-art.
