# LAD and Linear Programming

• Peter Bloomfield
• William L. Steiger
Part of the Progress in Probability and Statistics book series (PRPR, volume 6)

## Abstract

In this chapter we discuss the linear programming (LP) problem and its connection with LAD fitting. To fix the language and notation let there be given vectors c ∈ Rn, b ∈ Rm and an m by n matrix A. The vector c determines a linear functional f(x) = <c,x> on Rn and A and b determine m linear inequalities Axb. The LP problem in standard form is to
$$\begin{array}{*{20}{c}} {\max imize{\kern 1pt} f\left( x \right)} \\ {subject{\kern 1pt} to{\kern 1pt} A{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{x}} \leqslant b} \\ {{\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{x}} \geqslant 0} \\ \end{array}$$
(1)

## Keywords

Linear Programming Problem Simplex Method Slack Variable Iteration Count Simplex Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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