Closed-Form Expressions for Projectors onto Polyhedral Sets in Hilbert Spaces

Abstract

We provide formulas for projectors onto a polyhedral set, i.e., the intersection of a finite number of half-spaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly sufficient and necessary optimality conditions. This approach has already been successfully applied in deriving formulas for projection onto the intersection of two half-spaces. We also discuss possible generalizations to Banach spaces.