Incorrect values when calculating the optimum value using while loop

Dear all,

Please I'm trying to get the optimum power allocation Pk using while loop.. but it seems that I wrongly writing this algorithm and all values are equal to 1 without making alot of iterations... please can any one help me to correct the code.. I appreciate your help.

This is my code:

%parameters
TN=10
lamda=[5.3899,2.8511,1.0846,0.4003,2.8364,0.0988,0.0470,0.3417,0.5460,0.5992];
segma_squared=10^-9; %variance
tau=0.1; 
Pt=1;
beta= [0.3414,0.1707,0.1138,0.0854,0.0683,0.0569,0.0488,0.0427,0.0379,0.0341];
epsilon=0.001
%%%%%%%%%%%starting of algorithm 1%%%%%%%%%%%%%%%
max_iterations=1000;
power_allocation_initial=[5.3899,4.435,1.1024,0.4004,2.854,0.109988,0.0470,0.3417,0.3450,0.6592];
for i=2:max_iterations
    for k=1:TN
        gamma_infinity(i,k)=(lamda(k)*(1-tau^2)*power_allocation_initial(k)*Pt)/(segma_squared); % calculation initial value of gamma_inf(0)
        w_k(k)=log2(power_allocation_initial(k));
        while (gamma_infinity(i,k)-gamma_infinity(i-1,k) >= epsilon)
            i=i+1;
            gamma_infinity(i,k)=gamma_infinity(i-1,k);
            k_(k)=(gamma_infinity(i,k))/(1+gamma_infinity(i,k));
            v_k(k)=log2(1+gamma_infinity(i,k))-((gamma_infinity(i,k))/(1+gamma_infinity(i,k)))*log2(gamma_infinity(i,k));
            eita_wk(i,k)=-k_(k) *w_k(k)-k_(k)*log2(lamda(k)*(1-tau^2))*Pt + 2*k_(k)*log2(sqrt(segma_squared))-v_k(k); 
            w(i,k)=beta(k)*eita_wk(i,k);
            ww(i)=sum(w(i,k));
            [p_opt(k),fval] = linprog(ww(i),[],[],[],[],0,1);
        end
    end
end

[Torsten]

It would be helpful to know what problem (25) is.

[bassant tolba]

Thanks alot Torsten, I updated it and inerted problem 25

[Torsten]

You do the same mistake as before:

You try to decouple the problem and minimize one single ww(k):

[p_opt(k),fval] = linprog(ww(i),[],[],[],[],0,1);

although you are told to minimize sum(beta_k*gamma(ww(k))

So in short: Delete the loop over k - all values p(k) for k in K (so the complete vector p) have to be determined simulaneously by solving your optimization problem.

[bassant tolba]

Dear Torsten,

Thank you really for your reply. I modified the last two lines, but it says that the solution is unbounded and there is no values for p_opt

%parameters

TN=10

lamda=[5.3899,2.8511,1.0846,0.4003,2.8364,0.0988,0.0470,0.3417,0.5460,0.5992];

segma_squared=10^-9; %variance

tau=0.1;

Pt=1;

beta= [0.3414,0.1707,0.1138,0.0854,0.0683,0.0569,0.0488,0.0427,0.0379,0.0341];

epsilon=0.001

%%%%%%%%%%%starting of algorithm 1%%%%%%%%%%%%%%%

max_iterations=1000;

power_allocation_initial=[5.3899,4.435,1.1024,0.4004,2.854,0.109988,0.0470,0.3417,0.3450,0.6592];

for i=2:max_iterations

for k=1:TN

gamma_infinity(i,k)=(lamda(k)*(1-tau^2)*power_allocation_initial(k)*Pt)/(segma_squared); % calculation initial value of gamma_inf(0)

w_k(k)=log2(power_allocation_initial(k));

while (gamma_infinity(i,k)-gamma_infinity(i-1,k) >= epsilon)

i=i+1;

gamma_infinity(i,k)=gamma_infinity(i-1,k);

k_(k)=(gamma_infinity(i,k))/(1+gamma_infinity(i,k));

v_k(k)=log2(1+gamma_infinity(i,k))-((gamma_infinity(i,k))/(1+gamma_infinity(i,k)))*log2(gamma_infinity(i,k));

eita_wk(i,k)=-k_(k) *w_k(k)-k_(k)*log2(lamda(k)*(1-tau^2))*Pt + 2*k_(k)*log2(sqrt(segma_squared))-v_k(k);

w(i,k)=beta(k)*eita_wk(i,k);

end

end

ww=sum(w);

[p_opt,fval] = linprog(ww,[],[],[],[],0,1);

end

[Torsten]

Don't you see from the description of the algorithm that the optimization problem has to be solved within the while-loop and not outside ?

And now that you search for a vector p of length 10, your upper and lower bounds also have to be vectors of length 10. But you set them to 0 and 1 - so just one value.

And what is the for-loop good for ? Isn't it a superfluous duplicate of the while-loop ?

[bassant tolba]

Dear Torsten,

please can you kindly let me know by code, how to modify my code as I got confused sorry..

With regards to for loop, I used it to be able to do j-1 as a previous step

Answer 1

[Torsten]

With regards to for loop, I used it to be able to do j-1 as a previous step

But the steps (variable i) are done in the while loop - so no further for loop is needed.

I don't understand the underlying problem. Here is a suggestion for code as I understand the algorithm (although problem (25) is quite strange since the extra terms (2nd and 3rd) in the definition of Gamma don't depend on the optimization variable omega):

TN=10;
lamda=[5.3899,2.8511,1.0846,0.4003,2.8364,0.0988,0.0470,0.3417,0.5460,0.5992];
segma_squared=10^-9; %variance
tau=0.1; 
Pt=1;
beta= [0.3414,0.1707,0.1138,0.0854,0.0683,0.0569,0.0488,0.0427,0.0379,0.0341];
epsilon=0.001;
power_allocation_initial=[5.3899,4.435,1.1024,0.4004,2.854,0.109988,0.0470,0.3417,0.3450,0.6592];
gamma_infinity_im1=(lamda.*(1-tau^2).*power_allocation_initial*Pt)/(segma_squared); % calculation initial value of gamma_inf(0)
imax = 20;
i = 0;
error = 1;
while error > epsilon && i < imax
  i = i+1;
  kappa = gamma_infinity_im1./(1+gamma_infinity_im1);
  v = log2(1+gamma_infinity_im1)-kappa.*log2(gamma_infinity_im1);
  f = -beta.*kappa;  % Don't know if there are other terms in gamma(omega) that depend on p except the first
  omega = linprog(f,[],[],[],[],-Inf(10,1),log2(Pt)*ones(10,1));
  P = 2.^omega
  gamma_infinity_i = lamda.*(1-tau^2).*P.'*Pt/segma_squared;
  error = sum(abs(gamma_infinity_im1-gamma_infinity_i))
  gamma_infinity_im1 = gamma_infinity_i;
end

Optimal solution found.

P = 10×1

1 1 1 1 1 1 1 1 1 1

error = 3.9584e+10

Optimal solution found.

P = 10×1

1 1 1 1 1 1 1 1 1 1

error = 0

[bassant tolba]

Yeah your answer is correct ..thanks alot.. but, due to kappa and v are dependent on power in gamma_infinity so they are implicitly depend on omega as well. Thus, the objective function f should be = beta.*(-kappa * omega)- kappa* log2(lamda)*(1-tau^2)*Pt+2*kappa*log2(segma)-v

[Torsten]

I'm quite sure we both still don't understand the model correctly.

So I suggest you let the MATLAB code pause for a while and read the background article from which the algorithm was developed again carefully.

Do you have a link to the article in question ?

[bassant tolba]

yes sure,

here is the link for the article.

Really, I'm grateful for your help.

joint_service_caching_computing.pdf (soton.ac.uk)