Linear Programming: Basics, Simplex Algorithm, and Duality. Applications of Linear Programming: regression, classification and other engineering applications. Integer Linear Programming: Basics, ...

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 ...

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 ...

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