  Recently the primal-dual method of multipliers (PDMM), a novel distributed
optimization method, was proposed for solving a general class of decomposable
convex optimizations over graphic models. In this work, we first study the
convergence properties of PDMM for decomposable quadratic optimizations over
tree-structured graphs. We show that with proper parameter selection, PDMM
converges to its optimal solution in finite number of iterations. We then apply
PDMM for the causal estimation problem over a statistical linear state-space
model. We show that PDMM and the Kalman filter have the same update
expressions, where PDMM can be interpreted as solving a sequence of quadratic
optimizations over a growing chain graph.
