Easter 2010
Richard Weber
Optimization - Examples Sheet 2
1. Consider the three equations
2
1
A=
2
in 6 unknowns given by Ax = b where
1 1 1 0 0
2
,
5 .
2 3 0 1 0
b=
2 1 0 0 1
6
Choose B = cfw_1, 3, 6 and write Ax = b in the form AB xB + AN xN = b where
Easter 2010
Richard Weber
Optimization - Examples Sheet 1
1. Show how to solve the problem
n
min
i=1
1
(ai + xi )
n
subject to
xi = b,
xi 0 (i = 1, . . . , n)
i=1
where ai > 0, i = 1, . . . , n and b > 0.
2. Minimize each of the following functions in the