2
$\begingroup$

We can do local approximation with quadratic functions (with Hessian matrix). Is it important to have Hessian positive definite at the point? If quadratic approximation is not convex, does that hurt any in way?

$\endgroup$
5
  • 1
    $\begingroup$ Important for what? $\endgroup$
    – Aksakal
    Commented May 3, 2018 at 14:31
  • $\begingroup$ I am thinking "trust region method for optimization", but do not how to phrase it correctly. $\endgroup$
    – Haitao Du
    Commented May 3, 2018 at 14:33
  • $\begingroup$ Related question "Second derivative test for machine learning algorithms". $\endgroup$ Commented May 3, 2018 at 14:36
  • $\begingroup$ "trust region method for optimization" phrasing is fine. $\endgroup$
    – jbowman
    Commented May 3, 2018 at 15:17
  • $\begingroup$ so basically, when the hessian is positive definite, the geometric of the probability distribution over that point is convex, which means there is a local or global minima $\endgroup$
    – Rui
    Commented Mar 7, 2022 at 19:39

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.