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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 339
/
1
/
b
/
i
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Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 339
1
b
2026-09-28
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Solution
i
Solution
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i
The proximal optimality condition gives
t
x
k
−
x
k
+
1
∈
∂
f
(
x
k
+
1
)
.
(1)
The
subgradient inequality
therefore yields, for every
u
,
f
(
u
)
≥
f
(
x
k
+
1
)
+
t
1
(
x
k
−
x
k
+
1
)
T
(
u
−
x
k
+
1
)
.
(2)
Ancestors
(11)
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Paper 339
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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