I have been reading about convex optimization. We have:
minimize $f(x)$ s.t. $h(x) = 0$, $g(x) \le 0$, $x \in X$
It's Lagrangian dual is:
maximize $\phi(\lambda,\mu)$ s.t. $\mu \ge 0$, where $\phi(\lambda,\mu) = \inf[f(x) + \lambda' h(x) + \mu 'g(x)]$
I don't understand why $\mu$ must be greater than zero. Can anyone please explain?