# Sign restriction on the Lagrange multiplier? Why?

Say we are given a linear program where the goal is to minimize $c^Tx$ with the constraints $Ax\ge b$. Why is there a sign restriction on the Lagrange multiplier associated with the active constraints at the solution?

-

The gradient of $f(x_1,x_2,\ldots, x_n)$ is the vector $(\dfrac{\partial f}{\partial x_1}, \ldots, \dfrac{\partial f}{\partial x_n})$. –  Robert Israel May 14 '12 at 19:10
I can't comment the Robert Israel answer directly, but the gradient of the cost function would be $c^T$, and the gradient of the individual constraints would be the rows of $A$. –  vkubicki May 14 '12 at 19:06