Skip to main content
Theorem
Path
Curriculum
Paths
Labs
Diagnostic
Blog
Search
Sign in
Quiz Hub
/
Subgradients and Subdifferentials
Subgradients and Subdifferentials
5 selected
Difficulty 4-7
5 unseen
View topic
Intermediate
New
0 answered
3 intermediate
2 advanced
Adapts to your performance
Question 1 of 5
120s
intermediate (4/10)
state theorem
For a convex function
f
:
R
d
→
R
, a vector
g
∈
R
d
is a subgradient of
f
at
x
if what condition holds?
Hide and think first
A.
g
minimizes the directional derivative of
f
at
x
in some direction; subgradients are local steepest-descent directions.
B.
⟨
g
,
h
⟩
≤
f
(
x
+
h
)
−
f
(
x
)
for all
h
∈
R
d
with
∥
h
∥
=
1
; subgradients are unit-length differential operators.
C.
f
(
y
)
≥
f
(
x
)
+
⟨
g
,
y
−
x
⟩
for all
y
∈
R
d
; the linear function
h
(
y
)
=
f
(
x
)
+
⟨
g
,
y
−
x
⟩
is a global affine minorant of
f
touching at
x
.
D.
g
is the gradient of
f
at
x
,
g
=
∇
f
(
x
)
, defined wherever
f
is differentiable; subgradients are a synonym for gradients.
Submit Answer
I don't know