On the Projection onto a Finitely Generated Cone

Abstract

In the paper we study the properties of the projection onto a finitelygenerated cone. We show that this map is made up of finitely manylinear parts with a structure resembling the facial structure ofthe finitely generated cone. An economical regarding storage algorithmis also presented for calculating the projection of a fixed vector,based on Lemke's algorithm to solve a linear complementarity problem.Some remarks on the conical inverse a generalization of the Moore-Penrosegeneralized inverse conclude the paper.