Question

I don't understand why the curvature of a function with Hessian $H$ in a direction $p$ is $p^T H p$

score 111 · Answer 1 · 2026-03-29 04:26:23

111

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I don't understand why the curvature of a function with Hessian $H$ in a direction $p$ is $p^T H p$

Published on 29 Mar 2026 - 4:26

score 92 · Answer 2 · 2023-03-20 23:54:43

92

Views

Using the Hessian to determine convexity of $f(x,y) = \ln(x + y)$

Published on 20 Mar 2023 - 23:54

score 812 · Answer 3 · 2026-03-26 06:33:59

812

Views

Calculating L-smoothness constant for logistic regression.

Published on 26 Mar 2026 - 6:33

score 226 · Answer 4 · 2023-03-26 15:01:11

226

Views

Does Hessian of rank one mean curvature in one direction and flatness in the other

Published on 26 Mar 2023 - 15:01

score 57 · Answer 5 · 2026-03-25 06:30:33

57

Views

Is there any hope to find extrema points of the given function $f_z (x,y)$ without using the Hessian method?

Published on 25 Mar 2026 - 6:30

score 62 · Answer 6 · 2026-03-27 23:20:08

62

Views

Convexity of a function defined in spherical coordinates by $r=f(\theta,\phi)$

Published on 27 Mar 2026 - 23:20

score 45 · Answer 7 · 2023-04-08 00:48:08

45

Views

Incorrect quadratic expansion in gradient descent proof?

Published on 08 Apr 2023 - 0:48

score 57 · Answer 8 · 2023-04-14 15:08:38

57

Views

How to compute the Hessian of $x \mapsto |x|^{2p}$?

Published on 14 Apr 2023 - 15:08

score 99 · Answer 9 · 2023-04-14 23:26:30

99

Views

Constant Hessian is not symmetric?

Published on 14 Apr 2023 - 23:26

score 43 · Answer 10 · 2023-04-17 19:13:51

43

Views

Find values for the function convexity

Published on 17 Apr 2023 - 19:13

score 74 · Answer 11 · 2026-03-27 05:39:07

74

Views

It is true that $\|f\cdot \nabla^2f\|\leq \|\nabla f + \epsilon\|^2$?

Published on 27 Mar 2026 - 5:39

score 51 · Answer 12 · 2026-03-26 13:52:14

51

Views

How to prove $\left\Vert\nabla \frac{f}{||\nabla f||+\epsilon}\right\Vert\leq {\rm constant}$?

Published on 26 Mar 2026 - 13:52

score 313 · Answer 13 · 2026-03-25 15:12:12

313

Views

How can I prove the Hessian of the log likelihood of the Generalized Error Distribution is negative definite?

Published on 25 Mar 2026 - 15:12

score 65 · Answer 14 · 2023-04-29 09:40:28

65

Views

Find the local extemum of $x^{2}-2y^{2} - \ln (x + y)$

Published on 29 Apr 2023 - 9:40

score 176 · Answer 15 · 2023-04-29 18:45:10

176

Views

Second derivative of $\ell_p$ norm of a vector

Published on 29 Apr 2023 - 18:45

List Question

I don't understand why the curvature of a function with Hessian $H$ in a direction $p$ is $p^T H p$

Using the Hessian to determine convexity of $f(x,y) = \ln(x + y)$

Calculating L-smoothness constant for logistic regression.

Does Hessian of rank one mean curvature in one direction and flatness in the other

Is there any hope to find extrema points of the given function $f_z (x,y)$ without using the Hessian method?

Convexity of a function defined in spherical coordinates by $r=f(\theta,\phi)$

Incorrect quadratic expansion in gradient descent proof?

How to compute the Hessian of $x \mapsto |x|^{2p}$?

Constant Hessian is not symmetric?

Find values for the function convexity

It is true that $\|f\cdot \nabla^2f\|\leq \|\nabla f + \epsilon\|^2$?

How to prove $\left\Vert\nabla \frac{f}{||\nabla f||+\epsilon}\right\Vert\leq {\rm constant}$?

How can I prove the Hessian of the log likelihood of the Generalized Error Distribution is negative definite?

Find the local extemum of $x^{2}-2y^{2} - \ln (x + y)$

Second derivative of $\ell_p$ norm of a vector

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