Let $f,g: \mathcal{X} \to \mathbb{R}$. Let $f$ and $g$ be concave. We want to solve the following opitmization problem \begin{align} \max_{x \in \mathcal{X}} f(x) \\ \text{ s.t. } g(x) \le c \end{align} where $c\ge 0$.
My question: Since $g(x)$ is not convex the above problem does not fall into the category of convex optimization.
Keeping the above in mind, would the Lagrangian approach still given a neccesary codition on the optimality?
That is if we define \begin{align} L(x)=f(x)-\lambda (c-g(x)) \end{align}
then the optimall solution must be a stationary point of $L(x)$?