Linear Programming

Primal & Dual

1. Form 1:

Primal:

$$\begin{align}max.&\quad\mathbf{c}^T \mathbf{x}&\\ s.t.&&\\ &\mathbf{A}\mathbf{x} \le \mathbf{b}&\end{align}$$

Dual:

$$\begin{align}min.&\quad\mathbf{b}^T\mathbf{x}&\\ s.t.&&\\ &\mathbf{A}^T\mathbf{x}=\mathbf{c}&\\ &\mathbf{x}\ge \mathbf{0}&\end{align}$$