The Homogenization Cone: Polar Cone and Projection.

Let C be a closed convex subset of a real Hilbert space containing the origin, and assume that K is the homogenization cone of C, i.e., the smallest closed convex cone containing C × { 1 } . Homogenization cones play an important role in optimization for the construction of examples and counterexamples. A famous examples is the second-order/Lorentz/“ice cream” cone which is the homogenization cone of the unit ball. In this paper, we discuss the polar cone of K as well as an algorithm for finding the projection onto K provided that the projection onto C is available. Various examples illustrate our results. [ABSTRACT FROM AUTHOR]