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The Hessian Matrix
The Hessian Matrix
4 questions
Difficulty 4-7
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state theorem
For a twice-differentiable function
f
:
R
n
→
R
, convexity is equivalent to a condition on the Hessian. Which condition is correct?
Hide and think first
A.
∇
2
f
(
x
)
has all diagonal entries non-negative at every point
x
in the domain
B.
∇
2
f
(
x
)
is positive definite at every point
x
in the domain
C.
∇
2
f
(
x
)
has non-negative trace at every point
x
in the domain
D.
∇
2
f
(
x
)
is positive semidefinite at every point
x
in the domain
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