Notes on Linear Programming: Part 1. The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints

Abstract : The determination of optimum solutions to systems of linear inequalities has assumed increasing importance as a tool for mathematical analysis of certain problems in economics, logistics, and the theory of games. This paper develops a theory for avoiding assumptions regarding rank of underlying matrices which has import in applications where little or nothing is known about the rank of some linear inequality system requiring solution.