A simplex algorithm—gradient projection method for nonlinear programming

Witzgall [8], commenting on the gradient projection methods of R. Frisch and J. B. Rosen, states: “More or less all algorithms for solving the linear programming problem are known to be modifications of an algorithm for matrix inversion. Thus the simplex method corresponds to the Gauss-Jordan method. The methods of Frisch and Rosen are based on an interesting method for inverting symmetric matrices. However, this method is not a happy one, considered from the numerical point of view, and this seems to account for the relative instability of the projection methods.” This paper presents an implementation of the gradient projection method which uses a variation of the simplex algorithm. A more detailed exposition is given in [5]; motivation for this approach may be found in [6].