Algorithm for Least Squares Projections Onto the Intersection of Shifted, Convex Cones

摘要

A commonly occurring problem is that of minimizing least squares expressions subject to restrictions on the solution. Dykstra has given a simple algorithm for solving these types of problems when the constraint region can be expressed as a finite intersection of closed, convex cones. Here it is shown that this algorithm must still work correctly even when each cone is allowed to be arbitrarily translated (as long as the intersection is non-empty). This allows the algorithm to be applied to a much larger collection of problems than previously indicated. (Author)