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) = on Rn and A and b determine m linear inequalities Ax ≤ b. 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)
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