Finite Convergence of Circumcentered-Reflection Method on Closed Convex Cones in Hilbert Spaces

TL;DR

This paper proves that the circumcentered-reflection method (CRM) converges in finite steps when applied to the intersection of two closed convex cones in Hilbert spaces, with applications to polyhedral sets in Euclidean spaces.

Contribution

It establishes the finite convergence of CRM for convex cones in Hilbert spaces and extends this result to polyhedral sets in Euclidean spaces.

Findings

CRM converges finitely for two convex cones in Hilbert spaces.

Finite convergence also holds for two polyhedral sets in R^n.

The results advance understanding of CRM's efficiency in convex optimization.

Abstract

We establish finite convergence of circumcentered-reflection method (CRM) for the case of intersection of two closed convex cones in a real Hilbert space. We apply this result to prove the finite convergence for two polyhedral sets in R^n.