Heinz H Bauschke, Francesco Iorio, Valentin R Koch (2013)
The Method of Cyclic Intrepid Projections: Convergence Analysis and Numerical Experiments FMI 2013 Conference proceedings:
Forum "Math-for-Industry" 2013 -The Impact of Applications on Mathematics-
pp. 187-200
The Method of Cyclic Intrepid Projections: Convergence Analysis and Numerical Experiments
Forum "Math-for-Industry" 2013 -The Impact of Applications on Mathematics-
Authors
Heinz H Bauschke, , Valentin R Koch
Details
Abstract
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.