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.
One of the ultimate goals is to prototype and validate novel parallel computing frameworks to enable the development of next generation high-performance, scalable software applications, capable of tackling the ever-increasing complexity of real world engineering, design and digital media challenges.