Does anyone have an idea of how to tackle the following maximization problem?
Maximize the function $ f(x,y,z) = x - y - \alpha z^2 $, $ \alpha > 0 $, under the following constraints:
- C1: $ x>0 $, $\:\: y>0 $, $\:\: 0<z<1 $
- C2: $ y - \frac{1}{2} x^2 + c_1x \geq 0 $, $\:\: c_1>0 $
- C3: $ y - \frac{1}{2} x^2 + \frac{1}{2} (c_2 - A z )^2 < 0 $, $\:\: c_2,A>0 $
I would be grateful for any help/suggestions! :)