  The convex feasibility problem asks to find a point in the intersection of a
collection of nonempty closed convex sets. This problem is of basic importance
in mathematics and the physical sciences, and projection (or splitting) methods
solve it by employing the projection operators associated with the individual
sets to generate a sequence which converges to a solution. Motivated by an
application in road design, we present the method of cyclic intrepid
projections (CycIP) and provide a rigorous convergence analysis. We also report
on very promising numerical experiments in which CycIP is compared to a
commercial state-of-the-art optimization solver.
