MATHEMATICS 116, FALL 2007
CONVEXITY AND OPTIMIZATION WITH APPLICATIONS
Assignment #10
Last modiﬁed: December 3, 2007
Due Thursday, December 6 at class. All these problems are relevant to the quiz
on that date.
1. Luenberger, Problem 7.14.1. This is an interesting question, but I am not
convinced that I have found any
x
(
t
) for which the Gateaux diﬀerential is
linear. To start, consider the linearity requirement, diﬃcult to meet, that
δf
(
x
;
h
) +
δf
(
x
;

h
) = 0
.
2. Luenberger, Problem 7.14.4.
3. Solve the campaign chest problem done in class for the case where, in
addition to interest on your balance, you get contributions at a unit rate
from a PAC, so that the amount the you need to contribute is only
˙
x
(
t
)

x
(
t
)

1.
4. Your local trash collectors have the motto, “Them that has, gets it taken
away,” and so if the pile of trash outside your room has size
x
(
t
), it gets
taken away continuously in such a way that ˙
x
(
t
) =

x
(
t
). This is not good
enough for you, since
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 Fall '09
 Math, Geometry, NonEuclidean Geometry, Hyperbolic geometry, Möbius transformation, Poincaré metric, Poincaré halfplane model

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