A Finitely Convergent Circumcenter Method for the Convex Feasibility Problem

SIAM Journal on Optimization, Volume 34, Issue 3, Page 2535-2556, September 2024.
Abstract. In this paper, we present a variant of the circumcenter method for the convex feasibility problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating half-spaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.