Skip to main content
Theorem
Path
Curriculum
Atlas
Paths
Labs
Diagnostic
Evidence
Blog
Search
Sign in
Pulse
/
Optimization
Optimization Pulse
Five questions across 7 topics. No timer.
1 / 5
Optimization
Question 1 of 5
foundation (2/10)
compare
A function
f
:
R
n
→
R
is
L
-LIPSCHITZ continuous when which condition holds for some constant
L
≥
0
?
Hide and think first
A.
f
is
C
∞
with all derivatives bounded by
L
. Smoothness in the differential-topology sense.
B.
f
is convex with Hessian eigenvalues bounded by
L
. Curvature constraint via the spectrum.
C.
∥∇
f
(
x
)
−
∇
f
(
y
)
∥
≤
L
∥
x
−
y
∥
. The GRADIENT is
L
-Lipschitz; the function is
L
-smooth.
D.
∣
f
(
x
)
−
f
(
y
)
∣
≤
L
∥
x
−
y
∥
for all
x
,
y
. Slope of
f
is bounded by
L
in every direction.
Show Hint
Submit Answer
I don't know