In this paper, we study the rate of convergence of the cyclic projection
algorithm applied to finitely many basic semi-algebraic convex sets. We
establish an explicit convergence rate estimate which relies on the maximum
degree of the polynomials that generate the basic semi-algebraic convex sets
and the dimension of the underlying space. We achieve our results by exploiting
the algebraic structure of the basic semi-algebraic convex sets.Comment: 35 pages, revision incorporating referees' comment