An iterative process for the feasibility-seeking problem with sets that are unions of convex sets

In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve as a modeling approach in fields of applications and from the ongoing recent research efforts to handle non-convexity in feasibility-seeking.