Finite convergence of a subgradient projections method with expanding controls

We study finite convergence of the modified cyclic subgradient projections (MCSP) algorithm for the convex feasibility problem (CFP) in the Euclidean space. Expanding control sequences allow the indices of the sets of the CFP to re-appear and be used again by the algorithm within windows of iteration indices whose lengths are not constant but may increase without bound. Motivated by another development in finitely convergent sequential algorithms that has a significant real-world application in the field of radiation therapy treatment planning, we show that the MCSP algorithm retains its finite convergence when used with an expanding control that is repetitive and fulfills an additional condition.