I dont't understand a proof for the second-order condition for convexity

Question

I find a proof [here] (http://mathhelpforum.com/advanced-math-topics/129503-second-order-condition-convexity.html).
But I don't understand the second part. For example, what does it mean to say

For the converse, if f is convex, then certain subdeterminants of the Hessian matrix satisfy certain conditions.

Are you unfamiliar with some of the terms? Are you not sure what conditions are being talked about? Where is it you are stuck? — Alex Becker, Jun 11 '12 at 06:57
Yes, maybe. I don't know what the two 'certain' in the sentence mean.@AlexBecker — cloudygoose, Jun 11 '12 at 07:26

score 0 · Answer 1 · answered Aug 28 '23 at 13:30

0

The second part is hard to understand because it is basically a tautology; I would not consider it a valid proof. The "certain conditions" they're talking about is the positive-definiteness of the Hessian.

Another reference is given here

answered Aug 28 '23 at 13:30

Zim

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I dont't understand a proof for the second-order condition for convexity

1 Answers1