Face Method with LU Factorization

Abstract

The face and dual face methods, introduced in the previous two chapters, involve orthogonal transformations. But from a practical point of view, many researchers prefer LU factorization. In this chapter, we derive the face method based on LU factorization. In the following sections, we derive the descent search direction first and then address such topics as the update of the face solution, pivot operation, and optimality test. Then we spend the other sections to formulate the face algorithm in the tableau form and in the revised form, respectively, before making final comments.