A projective algorithm for linear programming with no regularity condition

The combined phase I-phase II projective algorithm of de Ghellinck and Vial solves any linear programming problem in its primal-dual formulation, without assuming any regularity condition. The method does not require artificial variables and/or constraints. It consists simply in minimizing the sum of all primal and dual variables. The present note is an alternative to a recent proposal of Anstreicher.