Unbounded and Infeasible problem

1

I use CVX to sovle the following question

cvx_begin
variable W1(Nt1,Nt1,cluster1) semidefinite
variable W2(Nt2,Nt2,cluster2) semidefinite
variables m1(usertotal1,1) n1(usertotal1,1)
variables x1(usertotal1,1) x2(usertotal2,1) y1(usertotal1,1) y2(usertotal2,1)
for m=1:cluster1
for n=1:user1
fCompose1(:,:,(m-1)*user1+n)=diag(f1(:,(m-1)*user1+n))Adiag(f1(:,(m-1)*user1+n)’);
end
end
for l=1:cluster2
for s=1:user2
fCompose2(:,:,(l-1)user2+s)=diag(f2(:,(l-1)user2+s))Adiag(f2(:,(l-1)user2+s)’);
end
end
maximize( sum(x1)-sum(y1)+sum(x2)-sum(y2) )
subject to
for m=1:cluster1
for n=1:user1
real((a1(m,n)+eta1sum(a1(n+1:user1))+sum(a1(1:n-1)))(trace(H1(:,:,(m-1)user1+n)W1(:,:,m))+sigma1^2trace(W1(:,:,m)))+trace(H1(:,:,(m-1)user1+n)(sum(W1,3)-W1(:,:,m)))+sigma1^2trace(sum(W1,3)-W1(:,:,m))+trace(fCompose1(:,:,(m-1)user1+n)(sum(W2,3)))+1)>=exp(x1((m-1)user1+n));
real((eta1sum(a1(n+1:user1))+sum(a1(1:n-1)))(trace(H1(:,:,(m-1)user1+n)W1(:,:,m))+sigma1^2trace(W1(:,:,m)))+trace(H1(:,:,(m-1)user1+n)(sum(W1,3)-W1(:,:,m)))+sigma1^2trace(sum(W1,3)-W1(:,:,m))+trace(fCompose1(:,:,(m-1)*user1+n)*sum(W2,3))+1) <= exp(yStart1((m-1)user1+n))(y1((m-1)*user1+n)-yStart1((m-1)user1+n)+1);
end
end
for l=1:cluster2
for s=1:user2
real((a2(l,s)+eta2sum(a2(s+1:user2))+sum(a2(1:s-1)))*trace(fCompose2(:,:,(l-1)*user2+s)W2(:,:,l))+trace(fCompose2(:,:,(l-1)user2+s)(sum(W2,3)-W2(:,:,l)))+(l==1)(trace(H2(:,:,(l-1)*user2+s)sum(W1,3))+sigma1^2trace(sum(W1,3)))+1) >= exp(x2((l-1)user2+s));
real((eta2sum(a2(s+1:user2))+sum(a2(1:s-1)))*trace(fCompose2(:,:,(l-1)*user2+s)W2(:,:,l))+trace(fCompose2(:,:,(l-1)user2+s)(sum(W2,3)-W2(:,:,l)))+(l==1)(trace(H2(:,:,(l-1)*user2+s)sum(W1,3))+sigma1^2trace(sum(W1,3)))+1) <= exp(yStart2((l-1)user2+s))(y2((l-1)*user2+s)-yStart2((l-1)*user2+s)+1);
end
end
trace(sum(W1,3))<=pTotal1;
trace(sum(W2,3))<=pTotal2;
cvx_end

And I get the correct answer,but when I add three other constraints. The answer become failed.

cvx_begin
variable W1(Nt1,Nt1,cluster1) semidefinite
variables m1(usertotal1,1) n1(usertotal1,1)
variables x1(usertotal1,1) x2(usertotal2,1) y1(usertotal1,1) y2(usertotal2,1)
expressions Z1(Nt1,Nt1,usertotal1) t1(Nt1,usertotal1) s1(usertotal1,1)
for m=1:cluster1
for n=1:user1
fCompose1(:,:,(m-1)*user1+n)=diag(f1(:,(m-1)*user1+n))Adiag(f1(:,(m-1)*user1+n)’);
Z1(:,:,(m-1)user1+n)=(a1(m,n)/gamma1-eta1sum(a1(n+1:user1))-sum(a1(1:n-1)))*W1(:,:,m)-(sum(W1,3)-W1(:,:,m));
t1(:,(m-1)*user1+n)=Z1(:,:,(m-1)*user1+n)’*deltaH1(:,(m-1)*user1+n);
s1((m-1)*user1+n)=-norm(ftotal1(:,(m-1)*user1+n)’*w_vector_max)^2-1;
end
end
for l=1:cluster2
for s=1:user2
fCompose2(:,:,(l-1)user2+s)=diag(f2(:,(l-1)user2+s))Adiag(f2(:,(l-1)user2+s)’);
end
end
maximize( sum(x1)-sum(y1)+sum(x2)-sum(y2) )
subject to
for m=1:cluster1
for n=1:user1
real((a1(m,n)+eta1sum(a1(n+1:user1))+sum(a1(1:n-1)))(trace(H1(:,:,(m-1)user1+n)W1(:,:,m))+sigma1^2trace(W1(:,:,m)))+trace(H1(:,:,(m-1)user1+n)(sum(W1,3)-W1(:,:,m)))+sigma1^2trace(sum(W1,3)-W1(:,:,m))+trace(fCompose1(:,:,(m-1)user1+n)(sum(W2,3)))+1)>=exp(x1((m-1)user1+n));
real((eta1sum(a1(n+1:user1))+sum(a1(1:n-1)))(trace(H1(:,:,(m-1)user1+n)W1(:,:,m))+sigma1^2trace(W1(:,:,m)))+trace(H1(:,:,(m-1)user1+n)(sum(W1,3)-W1(:,:,m)))+sigma1^2trace(sum(W1,3)-W1(:,:,m))+trace(fCompose1(:,:,(m-1)*user1+n)*sum(W2,3))+1) <= exp(yStart1((m-1)user1+n))(y1((m-1)*user1+n)-yStart1((m-1)*user1+n)+1);
real(trace(Z1(:,:,(m-1)user1+n))+s1((m-1)user1+n)) >= 2sqrt(log(1/prob1))(m1((m-1)*user1+n)+n1((m-1)*user1+n));
1/sqrt(2)*norm(t1(:,(m-1)*user1+n)) <= m1((m-1)user1+n);
u1norm(Z1(:,:,(m-1)*user1+n)) <= n1((m-1)*user1+n);

        end      
    end
    for l=1:cluster2
        for s=1:user2
            real((a2(l,s)+eta2*sum(a2(s+1:user2))+sum(a2(1:s-1)))*trace(fCompose2(:,:,(l-1)*user2+s)*W2(:,:,l))+trace(fCompose2(:,:,(l-1)*user2+s)*(sum(W2,3)-W2(:,:,l)))+(l==1)*(trace(H2(:,:,(l-1)*user2+s)*sum(W1,3))+sigma1^2*trace(sum(W1,3)))+1)  >=  exp(x2((l-1)*user2+s));
            real((eta2*sum(a2(s+1:user2))+sum(a2(1:s-1)))*trace(fCompose2(:,:,(l-1)*user2+s)*W2(:,:,l))+trace(fCompose2(:,:,(l-1)*user2+s)*(sum(W2,3)-W2(:,:,l)))+(l==1)*(trace(H2(:,:,(l-1)*user2+s)*sum(W1,3))+sigma1^2*trace(sum(W1,3)))+1)  <=  exp(yStart2((l-1)*user2+s))*(y2((l-1)*user2+s)-yStart2((l-1)*user2+s)+1);
        end
    end
    trace(sum(W1,3))<=pTotal1;
    trace(sum(W2,3))<=pTotal2;

cvx_end

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Unbounded

Status: Infeasible
Optimal value (cvx_optval): -Inf

I wonder that is this answer means a infeasible peoblem? or I can do some change?

2

I believe the dual is being solved and was assessed as unbounded. Hence the primal (i.e., your problem as entered) assessed to be infeasible, as reported by CVX Status.