  We propose finitely convergent methods for solving convex feasibility
problems defined over a possibly infinite pool of constraints. Following other
works in this area, we assume that the interior of the solution set is nonempty
and that certain overrelaxation parameters form a divergent series. We combine
our methods with a very general class of deterministic control sequences where,
roughly speaking, we require that sooner or later we encounter a violated
constraint if one exists. This requirement is satisfied, in particular, by the
cyclic, repetitive and remotest set controls. Moreover, it is almost surely
satisfied for random controls.
