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 ...

In this paper, a modification of the bisection simplex method is made for more general purpose use. Organized in an alternative simpler form, the modified version exploits information of the optimal ...

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.

The Interior-Point algorithm often solves network problems and linear programming (LP) problems much faster than the Simplex algorithm, and it can solve problems that are very large. LP problems that ...