Linear optimization

Linear optimization (or linear programming) is to minimize or maximize a linear function subject to a set of linear equality and inequality constraints. One example of an linear optimization problem is

$\begin{array}{lccr} \displaystyle{} \mbox{minimize}&\displaystyle{} c^{T} x &\displaystyle{} &\displaystyle{}\\ \displaystyle{} \mbox{subject to}&\displaystyle{} A x &\displaystyle{} = &\displaystyle{} b, \\ \displaystyle{} &\displaystyle{} x \geq{} 0. &\displaystyle{} &\displaystyle{}\\ \end{array}$