Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets

TL;DR

This paper investigates the convergence speed of the cyclic projection algorithm when applied to basic semi-algebraic convex sets, providing explicit estimates based on algebraic structure and polynomial degrees.

Contribution

It introduces a novel explicit convergence rate estimate for the cyclic projection algorithm tailored to semi-algebraic convex sets, leveraging their algebraic properties.

Findings

Convergence rate depends on polynomial degrees and space dimension.

Explicit rate estimates are derived based on algebraic structure.

Results improve understanding of algorithm efficiency for semi-algebraic sets.

Abstract

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.