A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces

Abstract

Many problems require the ability to find least squares projections onto convex regions. Here it is shown that if the constraint region can be expressed as a finite intersection of simpler convex regions, then one can obtain the projection onto the intersection by performing a series of projections only onto the simpler regions. This may facilitate finding least squares projections in more complicated spaces since the approach is valid for a general Hilbert space rather than just Rn.