In this paper we study the properties of the projection
onto a finitely generated cone. We show for example that this map is
made up of finitely many linear parts with a structure resembling the
facial structure of the finitely generated cone. An economical algorithm
is 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-Penrose
generalized inverse) conclude the paper
