Circumcentric directions of cones

Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, are enforced in a new setting; they proven provide inward directions sets given by convex inequalities. particular, we show that circumcentric of finitely generated cones belong the interior their polars. We also derive measure interiorness direction, which then provides special cone search directions, all being feasible region under consideration.