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 . 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  and , the authors study the capacity region variations and the optimal resource allocation scheme for the slowly fading
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