Find the critical points of the following constrained optimization problem
subject to
and check that they are non-degenerate. Determine the local minima and maxima.
My work:
Let
Lagrangian is
Then grad is equivalent to
(1)
=====>
=====>
(2)
(3)
with constraint
(4)
(1), (2), and (3) implies that
so with constraint (4) we have
so
Now I'm supposed to use the Hessian of L which I think is
and
This is where I get lost.....
I think I need to find the determinate of the bordered Hessian and find a tangent vector to somehow check if it is non-degenerate and determine the local minima and maxima.
Can anyone please help?
Thanks in advance.