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
The authors of REF provide general results on the convergence rate of APM for semi-algebraic sets.
Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets
arXiv: Functional Analysis
Computer Science Mathematics