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Convex Duality
Convex Duality
3 questions
Difficulty 5-6
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Intermediate
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intermediate (5/10)
state theorem
For a constrained optimization
min
f
(
x
)
subject to
g
(
x
)
≤
0
, the Lagrangian is
L
(
x
,
λ
)
=
f
(
x
)
+
λ
g
(
x
)
for
λ
≥
0
. What is the role of
λ
?
Hide and think first
A.
λ
is the dual variable (Lagrange multiplier); at optimum, it measures the sensitivity of the optimal value to constraint relaxation
B.
λ
is a step-size parameter that controls the learning rate during gradient-based optimization
C.
λ
is a free parameter of the objective; its value is arbitrary and doesn't affect the optimum
D.
λ
is an indicator that equals 1 if the constraint is active and 0 if inactive at the optimum
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