Linear programming with gradient-LP: A nonorthogonal projection gradient method

In 1986, research was started on a new method for linear programming. This method is derived from the projection gradient method proposed by Rosen in 1960, but it is different because the projection is not necessarily orthogonal. Thanks to this relaxation, updating the projection matrix is performed using a simple pivoting operation. First the main features of the method is recalled, then numerical and benchmark results are presented. Lastly, an overview is given of some industrial applications of the method which is beginning to be widely used in France.