I have the following optimization problem:
$$\min \frac{F}{A}+c_p D K \sqrt{A}+c_g \Theta^2+c_e a D + t e (1-\Theta) D+ \frac{t a}{A}$$
s.t. $a \leq [e (1-\Theta) D A] p_a$
$$\Theta \leq p_\Theta$$
$$\Theta, \quad A \geq 0, \quad A>0$$
Decision variables are $\Theta, A, a$.
Is it ok to solve this using KKT conditions? Are they ever necessary or sufficient or both? The first constraint is non linear. Is there a way to make it linear?
Or could I solve for the objective without the constraints and check if the constraints are satisfied? If a constraint is not then a would take the upper bound (for example).
For one variable version of this, without $\Theta$ and a, we can show that the objective has one root. Is there a way to do this for multiple variables?
Thank you,