Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex Sets

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 semialgebraic convex sets. 2010 Mathematics Subject Classification: Primary 41A25, 90C25; Secondary 41A50, 90C31