Mennucc

Convexity comment

Hi Andrea, I saw your comments on the discussion page of "convex function." I had written

If a function is twice continuously differentiable, then it is convex if and only if its second derivative is never negative (and it's strictly convex if in addition the second derivative is never zero). A strongly convex function's second derivative is bounded away from zero.

and you say

You are getting the definition of strictly convex wrong. (I have already corrected this same error before). The correct definition of strictly convex is in the article, and is the definition found in many books (such as link the rockafellar book).

Can you please be more specific and constructive? I think you are misunderstanding what I am saying. First of all, I am not giving a definition. To clarify what I mean: if a function has 2 continuous derivatives, then it is strictly convex if and only if the second derivative is strictly positive. This does not imply that a strictly convex function necessarily has 2 continuous derivatives, nor is it a definition. Lavaka (talk) 21:26, 11 March 2010 (UTC)

Dear Lavaka, I changed my comment to your comment. Mennucc (talk) 09:07, 14 May 2010 (UTC)