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Non-linear Optimization problem to maximize the sum-rate using fmincon

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Maheen Fazal
Maheen Fazal on 24 May 2019
Hi, kindly review my problem and suggest me a solution for it, i have been trying to solve this problem for 2weeks but am not able to find any solution that how should i solve this problem. In the main function code below all values are constant except phi(x), which i have to optimze.
the main function is given below, with fmincon code plus constraints.
function Rsumm= my_problem(x)
global n
Bn=2000;
Beta=0.3;
A=4000;
h=rand(1,n);
C=(0.0002224*h/(0.05*3.9811e-21));
R=((x*Bn)+A*log2(1+(1-Beta-x)*C));
Rsumm=-sum(R);
end
clear all
clc
global n
n_vec=2:2:8;
throughput=[];
for n=n_vec
initial_guess=0.00002;
x0=initial_guess;
lb=0.02;
ub=0.7;
A = [];
b = [];
Aeq=[];
Beq=[];
[x,fval]= fmincon(@(x) my_problem(x),x0,A,b,[],[],lb,ub,@my_constraint);
max=-(fval);
throughput=[throughput max];
end
plot(n_vec,throughput,'-b*')
function [c,ceq]=my_constraint(x)
c=my_problem(x)-20*1000;
ceq=[];
end
constraintss.PNG
in the above attached picture the author maximize the Rsum with two variables but i have to use only the highlighted one phi(x), and in constraints i mentioned the highlighted constraints.
the problem here is that the author used the over all sum of the equation for n number but in maximzation problem only phi (x) is considered. i am confused here and also donnot know how to solve this problem for this type of equation.
should i take x(n) in the function code?? and single x in fmincon code or try something different.

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