Duality

Abstract

In mathematical programming duality means that corresponding to every optimization (say minimization) problem, one relates a maximization problem in such a manner that by solving the latter problem it is possible to get the optimal value of the first one. To see the crucial ideas of this method let us consider a linear mathematical programming problem, denoted by (LP):

$$ \begin{gathered} \min {\kern 1pt} {\kern 1pt} cx \hfill \\ s.t.{\kern 1pt} x \in {R^{n}},{\kern 1pt} Ax \geqslant b \hfill \\ \end{gathered} $$

, where c ∈ Rⁿ, b ∈ R^m and A is an (n × m)-matrix.