One widely studied simplex variant, based on para- metric programming, is the shadow vertex algorithm of Borgwardt. This method is known to be exponen- tial in the worst case (see Goldfarb), but under ...

The death of mathematician George Dantzig is a scientific watershed. Dantzig developed "linear programming" and the simplex method, used to solve complex efficiency problems for large organizations.

In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve ...