  We consider the problem of minimizing a block separable convex function
(possibly nondifferentiable, and including constraints) plus Laplacian
regularization, a problem that arises in applications including model fitting,
regularizing stratified models, and multi-period portfolio optimization. We
develop a distributed majorization-minimization method for this general
problem, and derive a complete, self-contained, general, and simple proof of
convergence. Our method is able to scale to very large problems, and we
illustrate our approach on two applications, demonstrating its scalability and
accuracy.
