CO 350 Linear Optimization (Spring 2009)
TA’s comments for Assignment 2
Q1, Q2:
Most students got close but not many received full marks. A few common errors:
•
Not moving all constants in a constraint to the right hand side (e.g.

(4

2
x
3
)

x
2
≤ 
1).
•
Not including nonnegativity constraints. For example, in Q2, although it’s blatantly clear that
x
3
can only take positive values, it is still required to include
x
3
≥
0 to make it standard inequality
form.
•
Forgetting to ﬂip the sign of the RHS when reversing the sign of a constraint (e.g. turning
x
1
+
x
2
≥
1 into

x
1

x
2
≤
1).
•
In Q2, quite a few students took the constraint
x
2
≥
0 as a “real” constraint, and treated
x
2
as
a free variable. They substituted
x
2
=
u
2

v
2
and ended up capturing
x
2
≥
0 by

u
2
+
v
2
≤
0
,u
2
≥
0
,v
2
≥
0. While this is not “wrong”, it’s unnecessary and ineﬃcient in practice.
Q3:
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 Fall '07
 S.Furino,B.Guenin
 Optimization, TA, Mathematical optimization, Constraint, Candidate solution, Basic Feasible Solutions

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