# optimization of polynomial function with linear constraints

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.

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sorry what is actual question? – dato datuashvili Jul 3 '12 at 6:42
That function is polynomial only if $\alpha=0$ or $\alpha=1$. Are you sure that is what you mean? – Marc van Leeuwen Jul 3 '12 at 6:43
also what is linear constraints?can you add it? – dato datuashvili Jul 3 '12 at 6:43
Lagrange multipliers should work fine. The more explicit you make the problem, the more explicit the discussion can be. – André Nicolas Jul 3 '12 at 6:44
$f(x,y)$ surely is not a polynomial in general.You can't use quadratic programming for any $\alpha$. Lagrangian multiplies method is good for this type of problem or you can use any interior point method. – Aang Jul 3 '12 at 6:54