Let me reformulate my question

```
su=0;
cvx_begin
variable W_cvx(para.Nt,para.Nt,para.kc+para.ks) hermitian
variables miu4 miu3
variables etar zr vr vrp xr yr rrx rrv obj
Wall=zeros(para.Nt,para.Nt);
minimize(0)
subject to
for j=1:para.kc+para.ks
su=su+trace(W_cvx(:,:,j));
W_cvx(:,:,j) == hermitian_semidefinite(para.Nt);
Wall=Wall+W_cvx(:,:,j);
end
su<=para.pmax;
%%communication qos constraint
real( trace(Wall*Us(:,:,i))) >=(2^8-1)*real( trace( ( sum(W_cvx,3)-W_cvx(:,:,para.kc+1)) *Us(:,:,i)) +sigma_s);
for j=1:para.kc
real( trace(Wall*Uc(:,:,j,i)))>=(2^para.gama_c-1)*(real( trace( (Wall-W_cvx(:,:,j)) *Uc(:,:,j,i)))+sigma_c);
end
real( trace( Gur(:,:,i)'*Theta_t(:,:,i)'*te*te'*Theta_t(:,:,i)*Gur(:,:,i)*...
sum(W_cvx,3) ) )<= exp(z0(i,1))*(zr-z0(i,1)) -sigma_e;%C1
real( trace( Gur(:,:,i)'*Theta_t(:,:,i)'*te*te'*Theta_t(:,:,i)*Gur(:,:,i)*...
(sum(W_cvx,3)-W_cvx(:,:,para.kc+para.ks)) ) )-exp(vr)+sigma_e >=0;%C2
real( trace( Gur(:,:,i)'*Theta_t(:,:,i)'*hrs*hrs'*Theta_t(:,:,i)*Gur(:,:,i)*...
sum(W_cvx,3) ) )- exp(xr)+sigma_s>=0;%C3
real( trace( Gur(:,:,i)'*Theta_t(:,:,i)'*hrs*hrs'*Theta_t(:,:,i)*Gur(:,:,i)*...
(sum(W_cvx,3)-W_cvx(:,:,para.kc+para.ks)) ) )>=exp(y0(i,1))*(yr-y0(i,1))-sigma_s; %C4
cvx_end
```

output:

real( trace( Gur(:,:,i)'*Theta_t(:,:,i)‘*te*te’*Theta_t(:,:,i) Gur(:,:,i)…
sum(W_cvx,3) ) )<= exp(z0(i,1))*(zr-z0(i,1)) -sigma_e %C1

ans =

logical

1

real( trace( Gur(:,:,i)’*Theta_t(:,:,i)‘

*te*te’*Theta_t(:,:,i)

*Gur(:,:,i)*…

(sum(W_cvx,3)-W_cvx(:,:,para.kc+para.ks)) ) )-exp(vr)+sigma_e >=0 %C2

ans =

logical

0

Wall, zr, vr, xr,yr,rrx and rrv are variables,I did not put any restrictions on vr, xr,rrx,rrv,except for C2, C3. But the constraint C2 and C3 cannot be satisfied,C1 and c4 can, and I think that’s because the constraints are linear with respect to the variables coming in.

As you can see, I didn’t put any restrictions on vr and xr, except for C2, C3. we simply satisfied the constraints with equality. So I think it’s the strict function usage restrictions in cvx, but I can’t find a solution, what’s the problem?