On the Projection onto a finitely generated cone

Abstract

In the paper we study the properties of the projection onto a finitely generated cone. We show 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 (regarding storage) 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.