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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1Important for what? – Aksakal May 03 '18 at 14:31
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I am thinking "trust region method for optimization", but do not how to phrase it correctly. – Haitao Du May 03 '18 at 14:33
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Related question "Second derivative test for machine learning algorithms". – Richard Hardy May 03 '18 at 14:36
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"trust region method for optimization" phrasing is fine. – jbowman May 03 '18 at 15:17
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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 – Rui Mar 07 '22 at 19:39