The constraints are not fully satisfied

1

I have a convex problem that the following constraints are not fully satisfied. Moreover, the cvx_status is solved.
be=b_nkm.*e;
for m=1:M
be_temp= be(:,:,m);
be_t2=sum(be_temp,1);
for k=1:K
be_t2(:,k)-1<=0;
end
end

I will appreciate you if advise me.
The complete codes are as follows:

M=3;
N=2;
K=4;
E0=1;
N0=10^-16;
Bw=100e6;

pmax_r=2;
pr_max=pmax_rones(1,M);
min_user_rate=0;
e_avail=E0ones(1,K,M);
J_nor=10*rand(N,K,M);
landa=.5;
b_nkm(:,:,1)=[ 1 1 0 0;1 0 1 0];
b_nkm(:,:,2)=[ 1 0 1 0;1 1 0 0];
b_nkm(:,:,3)=[ 0 0 1 1;0 1 1 0];

p_rrh_old=(pmax_r/2)*ones(N,M);
alfa_old=[.6 .5 .7];

e_old=ones(N,K,M);

landa=.5;
R_rrh_min=.4;
e_old=.5ones(N,K,M);
rrh_fad=100rand(N,M);

cvx_begin
variables e(N,K,M) pr(N,M)

cnr=rrh_fad./(N0*Bw);
tr=log(1+cnr.*pr);
r_rrh=cvx(zeros(N,M));

for m=1:M
E_km=e_avail(:,:,m);
r_rrh(:,m)=((1-alfa_old(m))*tr(:,m));
for n=1:N

    for k=1:K
        check=J_nor(n,:,m)>=J_nor(n,k,m);       
        say= log(1+sum(((J_nor(n,:,m).*b_nkm(n,:,m).*e(n,:,m).*check.*E_km)/alfa_old(m)))+(J_nor(n,k,m)*b_nkm(n,k,m)*e(n,k,m)*E_km(1,k)));
        omega=alfa_old(m)*log(1+sum(((J_nor(n,:,m).*b_nkm(n,:,m).*e_old(n,:,m).*check.*E_km)/alfa_old(m))));
        
        for i=1:K
           if(i~=k)
               gerad_e=(J_nor(n,i,m)*b_nkm(n,i,m)*E_km(1,i))/(1+sum(((J_nor(n,:,m).*b_nkm(n,:,m).*e_old(n,:,m).*check.*E_km)/alfa_old(m))));
           else
              gerad_e=0; 
              omega_hat=omega+gerad_e*(e(n,k,m)-e_old(n,k,m));
              objfunc(n,k,m)=(say-omega_hat);
           end
           
        end
    end
end

end

maximize sum(sum(sum(objfunc)))+sum(sum(r_rrh))-(landa*sum(sum(pr)))
subject to
%constraint for the power of the rrh
for m=1:M
s=0;
for n=1:N
s=s+ pr(n,m);
end
s-pr_max(m) <=0;
end
%constraint for the rate of the rrh
for m=1:M
temp1=sum(tr,1);
R_rrh_min-temp1(:,m) <=0;
end
%constraint for the enegy of the user
be=b_nkm.*e;
for m=1:M
be_temp= be(:,:,m);
be_t2=sum(be_temp,1);
for k=1:K
be_t2(:,k)-1<=0;
end
end

%dc constraint

for m=1:M
   tdc1=objfunc(:,:,m);
    btemp=b_nkm(:,:,m);
    tdc=btemp.*tdc1;
   tdc2=sum(tdc,1);
   for k=1:K
       tdc2(k)-min_user_rate >= 0;
   end
end

  for m=1:M
    for n=1:N
        for k=1:K
            1>=e(n,k,m)>=0
        end
    end
  end
  
  for m=1:M
 for n=1:N
     pr(n,m)>=0;
 end

end
cvx_end

The output of “e” are as follows:

e(:,:,1) =

0.0000    1.0000    0.5000    0.5000
1.0000    0.5000    1.0000    0.5000

e(:,:,2) =

0.0483    0.5000    1.0000    0.5000
0.9517    1.0000    0.5000    0.5000

e(:,:,3) =

0.5000    0.5000    0.0000    1.0000
0.5000    1.0000    1.0000    0.5000

For example for the second column of “e(:,:,1)”, the values are 1 and .5 that their summation is more than one while the summation should be less than one.

Thanks.

2

Is there some applicable constraint other than

 for m=1:M
    for n=1:N
        for k=1:K
            1>=e(n,k,m)>=0
        end
    end
  end

That only constrains individual elements to be in [0,1], not their sums. All your output satisfies these constraints. I’m not sure what constraints you want, but use sum, specifying the summation across the dimension you want, for example,
1 >= sum(e,1) >= 0

Your constraints, as written, are equivalent to
1 >= e >= 0
which avoid the for loops. I leave you to determine whether you want such constraints on individual elements in addition to constraints on their sums.

3

Thank you for your advises, you are right, the constraint 1>=sum(e,1)>=0 should be added.
Best regards

4

Given what you want the constraints to be, you can avoid redundant constraints (which I don’t think would cause any harm , though) by using this pair of constraints.

e >= 0
1 >= sum(e,1)
5

Thank you for your kind advises.
Best regards