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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Important 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"](https://stats.stackexchange.com/questions/344212/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