  The Alternating Direction Method of Multipliers (ADMM) provides a natural way
of solving inverse problems with multiple partial differential equations (PDE)
forward models and nonsmooth regularization. ADMM allows splitting these
large-scale inverse problems into smaller, simpler sub-problems, for which
computationally efficient solvers are available. In particular, we apply
large-scale second-order optimization methods to solve the fully-decoupled
Tikhonov regularized inverse problems stemming from each PDE forward model. We
use fast proximal methods to handle the nonsmooth regularization term. In this
work, we discuss several adaptations (such as the choice of the consensus norm)
needed to maintain consistency with the underlining infinite-dimensional
problem. We present two imaging applications inspired by electrical impedance
tomography and quantitative photoacoustic tomography to demonstrate the
proposed method's effectiveness.
