Solving Composite Fixed Point Problems with Block Updates

Abstract Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only block at each iteration. In the more challenging class composite problems involving that do not share points, current methods require activation all iteration, and question maintaining convergence while updating blocks is open. We propose method achieves this goal analyze its asymptotic behavior. Weak, strong, linear results established exploiting connection with theory concentrating arrays. Applications several nonlinear nonsmooth analysis presented, ranging from monotone inclusions inconsistent feasibility problems, variational inequalities minimization arising in data science.