CO 355 Mathematical Optimization (Fall 2010)
Assignment 3
Due:
Tuesday, November 2nd, in class.
Policy.
No collaboration is allowed. You may use the course notes / textbook and the lecture slides, but
please be very speciﬁc
when using citing results found there. (Don’t just say “from some claim in class
we know.
...”.) Every other resource that you might stumble upon must be properly referenced. You are
welcome to seek help from the current instructor and TAs for CO 355.
Let
C
be a nonempty convex set. Let
A
be an aﬃne space such that
C
⊆
A
and dim
A
= dim
C
. In
fact,
A
is unique, and it is called the
aﬃne hull
of
C
. We say that a point
x
∈
C
is a
relative interior
point of
C
if there exists a closed ball
B
(
x,±
) centered at
x
of radius
± >
0 such that
B
(
x,±
)
∩
A
⊆
C
. (In
other words,
y
∈
A
and
k
x

y
k ≤
±
jointly imply
y
∈
C
.) The set of all relative interior points of
C
is
denoted ri(
C
). The relative interior is often very useful because ri(
C
) is nonempty and convex (assuming
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 Winter '10
 Harvey
 Interior, Closure, Polytope, Relative interior, nonempty convex

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