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?
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1$\begingroup$ Important for what? $\endgroup$– AksakalCommented May 3, 2018 at 14:31
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$\begingroup$ I am thinking "trust region method for optimization", but do not how to phrase it correctly. $\endgroup$– Haitao DuCommented May 3, 2018 at 14:33
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$\begingroup$ Related question "Second derivative test for machine learning algorithms". $\endgroup$– Richard HardyCommented May 3, 2018 at 14:36
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$\begingroup$ "trust region method for optimization" phrasing is fine. $\endgroup$– jbowmanCommented May 3, 2018 at 15:17
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$\begingroup$ 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 $\endgroup$– RuiCommented Mar 7, 2022 at 19:39
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