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 ...

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 ...

We prove that the classic policy-iteration method [Howard, R. A. 1960. Dynamic Programming and Markov Processes. MIT, Cambridge] and the original simplex method with the most-negative-reduced-cost ...

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

The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method, Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm.

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