Heinz Bauschke title: The method of reflection-projections for convex feasibility problems with an obtuse cone. abstract: The convex feasibility problem consists of finding a point in the intersection of closed convex sets. The classical method of cyclic projections approximates a solution by projecting cyclically onto the constraint sets. We consider the case when one of the constraints is an obtuse cone, e.g., the nonnegative orthant or the positive semidefinite matrices. We obtain a convergence result when the projection onto the cone is replaced by the reflection. Numerical experiments suggest that this approach is faster than the method of cyclic projections. We also comment on the inconsistent case. Based on joint work with Serge Kruk (Oakland University).