I have a polynomial function, which is actually the Cobb-Douglas production function, of the form $f(x,y) = \frac{\{x^{\alpha} y^{1-\alpha}\}^{1-\gamma}}{1-\gamma}$
with linear constraint
K(x,y)= Ax + By, (the constraint is more complicated that what is shown, but it is still a linear equation of this form)
and
$\alpha,\gamma \in (0,1)$
I'm thinking of using quadratic programming, but my function is not quadratic equation. Or Augmented Lagrangian method will be the most appropriate solution?
Thank you.