Recent literature in statistics, machine learning, and computer science has revisited the alternating direction method of multipliers (ADMM) algorithm for solving large-scale optimization problems. ADMM's computational utility often comes from the decomposition of the original objective into smaller subproblems, each of which depends on a subset of the original variables. It is therefore especially amenable to parallelization. However, objective functions involving large matrix operations may not be easily parallelizable. In this talk, we examine some situations where the subproblems still require large matrix computations and the effects of matrix sketching on solving these problems. Our work is specifically motivated by problems in the estimation of sparse subspaces and an application to variance estimation with large-scale climate satellite data.