On the finite convergence of a projected cutter method
  The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the fixed point set has nonempty interior. Our assumptions on the parameters are more general than existing ones. Various limiting examples and comparisons are provided. 
Heinz H. Bauschke, Caifang Wang, Xianfu Wang, Jia Xu
math.OC