diff --git a/notes/notes.org b/notes/notes.org index 913c734..eae8313 100644 --- a/notes/notes.org +++ b/notes/notes.org @@ -4184,7 +4184,7 @@ Assume \(f\) is smooth, i.e. has all needed derivatives. - Necessary: \(\nabla f (\B{x}^\ast ) = 0\) (i.e. \(\B{x}^\ast\) is an extremal point) - - Sufficient: \(\nabla f (\B{x}^\ast ) = 0\) and \(H_f (\B{x}^\ast )\) positive semidefinite + - Sufficient: \(\nabla f (\B{x}^\ast ) = 0\) and \(H_f (\B{x}^\ast )\) positive definite (implies \(x^\ast\) is a local minimum)