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.
IEEE/CAA Journal of Automatica Sinica
Corresponding author: Jonathan Tuck,is a Ph.D. candidate at StanfordUniversity in the Electrical Engineering Department.He received his B.S. degree in electrical engineeringfrom the Georgia Institute of Technology in 2016;David Hallac is a Ph.D. candidate at Stanford Universityin the Electrical Engineering Department. Hereceived his M.S. degree from Stanford in 2015 andhis B.S. degree from the University of Pennsylvaniain 2013;Stephen Boyd (F’99) is the Samsung Professor ofEngineering, and Professor of Electrical Engineeringin the Information Systems Laboratory at StanfordUniversity, with courtesy appointments in ComputerScience and Management Science and Engineering.