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In this paper, we present a variant of the circumcenter method for the ConvexFeasibility Problem (CFP), ensuring finite convergence under a Slaterassumption. The method replaces exact projections onto the convex sets withprojections onto separating halfspaces, perturbed by positive exogenousparameters that decrease to zero along the iterations. If the perturbationparameters decrease slowly enough, such as the terms of a diverging series,finite convergence is achieved. To the best of our knowledge, this is the firstcircumcenter method for CFP that guarantees finite convergence.

A finitely convergent circumcenter method for the Convex Feasibility Problem