the same value resulted from the linear optimization problem

Hello everyone,

I'd like to get the optimized value of w_k for a number of " k" users.. in objfun_25 as shown below. I got the value of " w_k" for all k users equal to zero (w_optimized in the below code).. and this is not logic..

can anyone help me to know ehere is the error in my code ?

w_k = optimvar('w_k',10,'Type','continuous','LowerBound',-Inf,'UpperBound',0);

k_=[1,1,1,1,1,1,1,1,1,1];

Pt=1;

lamda=[ 1.4856,0.4647,0.0276,1.1583,0.9820,0.2113,0.5524,0.6909,0.1797,0.3763];

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

tau=0.1;

segma_squared=10^-9;

v_k=[0.0145,0.0461,0.6900,0.0194,0.0227,0.0989,0.0394,0.0318,0.1154,0.0569];

for k=1:10

eita_wk(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(k)=beta(k)*eita_wk(k);

end

objfun_25=sum(w);

ProCach3=optimproblem; % create an optimization problem

ProCach3.Objective=objfun_25; %minimization equation

opts3=optimoptions('linprog','Display','off','MaxTime',3600*12);

[sol3,fval3,exitflag3,output3]=solve(ProCach3,'Options',opts3)

w_optimized=sol3.w_k;

Thank you very much

Answer 1

[Torsten]

You define

w(k)=beta(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)); 

and want to minimize the sum over k of this expression with respect to w_k where you set the constraint as -Inf < w_k(k) <= 0.

Now if you multiply out the expression for w(k), you can write

w(k) = beta(k)*(-k_(k)) w_k(k) + beta(k)*(-k_(k)*log2(lamda(k)*(1-tau^2))*Pt + 2*k_(k)*log2(sqrt(segma_squared))-v_k(k))
     = T1 + T2

with

T1 = beta(k)*(-k_(k)) w_k(k)

and

T2 = beta(k)*(-k_(k)*log2(lamda(k)*(1-tau^2))*Pt + 2*k_(k)*log2(sqrt(segma_squared))-v_k(k))

T2 does not depend on w_k(k), so it can be discarded in the optimization for w_k.

So you try to find w_k such that

sum(beta(k)*(-k_(k))*w_k(k))

is minimized where -Inf < w_k <=0.

Now beta and k_ are both >=0 and w_k is constrained to be <= 0.

Thus the sum is minimized (with value 0) if w_k(k) = 0 for all k.

[bassant tolba]

Dear Torsten,

Thank you very much for your clarification.

I got it thanks alot.

So in your opinion, is there a specific parmeter I can change to get change in the w_optimized ??

[Torsten]

So in your opinion, is there a specific parmeter I can change to get change in the w_optimized ??

You could maximize sum(w).

Or you could change the constraints on w(k) to 0 <= w < Inf.

But if the problem you posted is the one you have to solve, you cannot just change it ...

My advice: try to understand the IT-background of the optimization problems in your article - this is the only way to succeed. For me as an outstanding person who has no knowledge of what the authors talk about, the article appears to be very difficult to understand.

[bassant tolba]

Yeah.. you are right..

I will insha Allah

Thank again really for your help.. I deeply apprecitae that

[Torsten]

Good luck !