Contextes de border pour le sens abstrait
A bordered Hessian is used for the second-derivative test in certain
constrained optimization problems. Given the function as before:
--
the bordered Hessian appears as
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If there are, say, m constraints then the zero in the north-west corner
is an m × m block of zeroes, and there are m border rows at the top and
m border columns at the left.
The above rules of positive definite and negative definite can not
apply here since a bordered Hessian can not be definite: we have z'Hz =
0 if vector z has a non-zero as its first element, followed by zeroes.
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The second derivative test consists here of sign restrictions of the
determinants of a certain set of n - m submatrices of the bordered
Hessian.^[2] Intuitively, think of the m constraints as reducing the