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 ...

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.

A version of a two-phase simplex technique is given for manually solving those linear-programming problems in which artificial vectors are introduced and subsequently driven out. The first phase of ...

Linear programming -- which is not related to computer programming -- and the Simplex Algorithm provide a means for solving complicated problems with many variables and are generally employed to ...