2020/08/11 by Edgar Matias, Matias, Edgar, Majela Pentón Machado +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2008.04831
openalex publication_date 2020/08/11 · openalex created_date 2020/08/18 · openalex updated_date 2026/07/28
In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random iteration of paracontraction maps driven by an ergodic stationary sequence converges, with probability one, to a solution of the stochastic feasibility problem, provided a solution exists. As applications, we obtain non-white noise randomized algorithms to solve the stochastic convex feasibility problem and the problem of finding an almost surely common zero of a collection of maximal monotone operators.