On local convergence of the method of alternating projections

TL;DR

This paper proves local convergence of the method of alternating projections between subanalytic sets under mild regularity conditions, with a convergence rate of O(k^{- ho}).

Contribution

It establishes the local convergence and convergence rate of alternating projections between subanalytic sets under mild regularity assumptions.

Findings

Convergence is guaranteed locally under mild regularity.

The convergence rate is polynomial, specifically O(k^{- ho}).

Applicable to subanalytic sets, broadening classical results.

Abstract

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets $A,B$ under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O$(k^{-\rho})$ for some $\rho\in (0,\infty)$.