second order condition
From: Dusan (dusan.bednarik_at_uhk.cz)
Date: 06/24/04
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Date: Thu, 24 Jun 2004 17:00:41 +0000 (UTC)
Hi!
I would like to know if the following assertion is true or not :
Let f be a function defined on a Banach space X, f has
a Frechet derivative f' of the first order on a neighbourhood
of some point x\in X and have
second-order Gateaux derivative D^2 f(x) at the point x.
If f'(x)=0 and
there is c>0 s.t.
for any h\in X it holds : D^2 f(x)[h,h]>= c*|h|^2,
then f attains a strict local minimum at the point x.
If this is not true, find some counterexample.
Thank you in advance. Dusan
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