Moreover, a new, ratio-test-free pivoting rule is proposed, significantly reducing computational cost at each iteration. Our numerical experiments show that the method is very promising, at least for ...

The Simplex Method To develop a general solution method, let's look carefully at the solution of the two-variable problem: First, we need to introduce some definitions. We will refer to any assignment ...

We propose a new decomposition method for large-scale linear programming. This method dualizes an (arbitrary) subset of the constraints and then maximizes the resulting dual functional by dual ascent.

About the same time, he invented the “simplex method,” an algorithm for solving linear programming problems.