Linear Systems and Inverse Projection

Abstract

The projection process replaces variables with constraints. In this chapter, we study the inverse, or dual of projection, and replace constraints with variables. Our development is based primarily on Dantzig and Eaves [109] and Williams [453]. Replacing constraints with variables is illustrated next in Section 3.2. We refer to the process of replacing constraints with variables as inverse projection. This is logical because in projection we replace variables with constraints. In Section 3.2 we also show how to solve linear programs with inverse projection and give a simple proof of the finite basis theorem for polyhedra. In Section 3.3 we further illustrate the duality between projection and inverse projection. Sensitivity analysis of the objective function coefficients is covered in Section 3.4. Concluding remarks are given in Section 3.5. Exercises are provided in Section 3.6.