Hi, I have an optimization question that should be solved with the constraints which are written. λ is a constant greater than one and ρ is total power budget that we have.

Total Power Constraint: Let ρ be a given constant, and it is referred to as the total power budget. Solve the following optimization problem:

max Rb( ρ1 ,ρ2 )
Rb = (1 + 1/( λ- 1))log2(1 +β1*ρ1/(1 +β2*ρ2)) 
subject to the following constraints: 
ρ1 +ρ2 ≤ρ
β1  , β2 > 0
ρ1 ,ρ2 ≥ 0
ρ=constant & λ> 1 ,constant

[Torsten]

beta1, beta2 are given constants or free variables ?

[Sajjad Emdadi]

β1,β2 are two given sets of values

Answer 1

[Walter Roberson]

Make β1 infinite and ρ1 ,ρ2 > 0 . Then 1+β1*ρ1/(1 +β2*ρ2) will be infinite, and log2() of that will be infinite, so Rb will be infinite.

[Sajjad Emdadi]

β1, β2 are two constant given values, I should find a relation between ρ1,ρ2 based on value that ρ has to maximize the function. below is question:

Total Power Constraint: Let ρ be a given constant, and it is referred to as the total power budget. Solve the following optimization problem. subject the following constraint ρ1 +ρ2 ≤ρ.

Answer 2

[Torsten]

Solution is simple:

rho1 = rho, rho2 = 0.