  This work is concerned with the optimization of nonconvex, nonsmooth
composite optimization problems, whose objective is a composition of a
nonlinear mapping and a nonsmooth nonconvex function, that can be written as an
infimal convolution (inf-conv). To tackle this problem class we propose to
reformulate the problem exploiting its inf-conv structure and derive a block
coordinate descent scheme on a Bregman augmented Lagrangian, that can be
implemented asynchronously. We prove convergence of our scheme to stationary
points of the original model for a specific choice of the penalty parameter.
Our framework includes various existing algorithms as special cases, such as
DC-programming, $k$-means clustering and ADMM with nonlinear operator, when a
specific objective function and inf-conv decomposition (inf-deconvolution) is
chosen. In illustrative experiments, we provide evidence, that our algorithm
behaves favorably in terms of low objective value and robustness towards
initialization, when compared to DC-programming or the $k$-means algorithm.
