Set Regularities and Feasibility Problems
  We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms. 
Alexander Y. Kruger, D. Russell Luke and Nguyen H. Thao
math.OC