In this talk, we study the rate of convergence of the cyclic projection algorithm applied to finitely many semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the semi-algebraic convex sets.

This is the joint work with Jon Borwein and Guoyin Li.