Linear Programming

Abstract

Linear programming deals with the optimization of systems of linear equations subject to linear constraints. The problem is first exposed with the introduction of slack and artificial variables. The solution is treated by means of the simplex tableau in different cases. The theoretical solution is demonstrated as well as numerical examples. The duality is discussed mathematically and also explained by examples. Interior point methods are first introduced with Karmarkar’s projection method and algorithm, followed by the affine transformation. All algorithms are accompanied by numerical examples.