- #1
mathmari
Gold Member
MHB
- 5,049
- 7
Hey! :giggle:
We have the function and the function .
I have shown that has a local minimumat
I want to show that has not a local minimum in .
The gradient is Acritical point is , since .
The Hessian matrix is
The matrixin in is
The eigenvalues are, , . These are non-negativ, so the Hessian matrix is positiv semidefinite.
That means that has in either a minimum or a saddle point.
Is that correct so far? Now we have to show that in has a sddle point and not a minimum, right? But how? :unsure:
We have the function
I have shown that
I want to show that
The gradient is
The Hessian matrix is
The matrixin in
The eigenvalues are,
That means that
Is that correct so far? Now we have to show that in