Can KKT be used in minimization s.t to constant param

Question

Can KKT be used :

min g(x)

s.t x>=constant
where constant > 0

I have read this

The Kuhn-Tucker method: here says that

This is an alternative, and slightly simpler method for dealing with the common case where there are positivity constraints, that is constraints of the form xi ≥ 0 or − xi ≤ 0.

Answer 1

Minimizing $g(x)$ is equivalent to maximizing $-g(x)$. So, you can restate your initial problem as

$$ \max_{x} -g(x) \quad s.t. \; x \ge a \quad ,\text{ where } a \text{ is some constant}$$

and use the standard KKT method.