# Questions tagged [hessian]

The hessian tag has no usage guidance.

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### Does $f$ have the same minimiser as $\|\nabla f \|$ for $f$ strictly convex?

This question is migrated from MathStackExchange where it seemed to be too hard. I wonder does anyone here have any ideas?
Suppose $f: K \to \mathbb R$ is $\mathcal C^2$ and strictly convex on some ...

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### Product of concave functions and harmonic mean

I discovered something interesting, and I would like to know whether it is a known result or not. Say that a function $f: \Omega \subset \mathbb{R} \rightarrow \mathbb{R_+^*}$ is $\alpha$-concave if $...

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### Factoring certain Hessians of real homogeneous bivariate polynomials

For any homogeneous polynomial $f \in \mathbb R [x,y]$, define the homogeneous polynomial
$$H(f) := \partial_yf^2\partial_x\partial_xf-2\partial_xf\partial_yf\;\partial_x\partial_yf+\partial_xf^2\...