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20
where
α
+
β
=
1,
α
≥
0,
β
≥
0
…(E12)
Moreover, the Least Squares method and Linear Programming are special cases of convex
optimization. The Least Squares method tries to minimize
Ax – b
2
while the problem of Linear
Programming is defined as follows:
Minimize c
T
x with the constraints a
T
x
≤
b
i
for i
=
1,…,m
…(E13)
Unfortunately, sometimes the function that needs to be optimized is not convex. In this case, the
algorithms used to carry out the optimization are slow and complex. To overcome such a
problem, researchers often use heuristics, intuitions and approximations to reduce the
algorithmic complexity of the optimization procedure. Readers who are interested in the details
of Convex Optimization should refer to [22].
3.3 Resource Allocation In Multiuser Wireless Systems
Dr. Andrea Goldsmith at Stanford University has done extensive work with some of her students
on resource allocation in multiuser wireless systems. In [23] and [24], the authors study the
capacity region variations and the optimal resource allocation scheme for the slowly fading
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 Spring '09
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