Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings

. We present a parallel computing proximal method for solving the problem of minimizing the sum of convex functions over the intersection of fixed point sets of quasi-nonexpansive mappings in a real Hilbert space. We also provide a convergence analysis of the method for constant and diminishing step sizes under certain assumptions as well as a convergence-rate analysis for a diminishing step size. Numerical comparisons show that the performance of the algorithm is comparable with existing subgradient methods.