ouss
(Maîtrise en télécommunications)
April 11, 2017, 4:44pm
1
Hello,

I am trying to solve this problem with CVX tool but I have one error that I can’t resolve.
My Matlab code is:

cvx_begin
variable alph
variable bet(M,1)
expression bett(M,M)
Bett = diag(bet);
variable u(M,1)
expression U(M,M)
%U = u*u’;
for i =1:M
for j=1:M
U(i,j) = conj(u(i))u(j);
end
end
expression ppp(M,1)
for i=1:M
ppp(i) = u(i)conj(u(i));
end
vv = sum(ppp);
minimize( alph rho mean(N) - sum(bet.*p.*g.*conj(g).l.conj(l)) )
subject to
alph M tho^2>=vv;
alph>=0;
u>=0;

BB = G + Bett - Ps*(alph*(hchc’) + U + u hc’ + hcu’);
for i=1:M
B = zeros(M,M);
B(i,i)=sqrt(N(i))/abs(g(i));
BB = BB + rho B*(alphhc hc’ + U + uhc’ + hc u’)*B;
end
BB >= 0;
bet > 0;
cvx_end

The error that keeps showing is:

Error using cvx/times (line 262)
Disciplined convex programming error:
Invalid quadratic form(s): not a square.

Error in cvx/mtimes (line 36)
z = feval( oper, x, y );

Error in robust (line 68)
U(i,j) = (u(i))*u(j);

I tried to define U element by element but it’s not working. Can you please help me figure this out I am out of solutions.

Thank you.

`u(i)*u(j)`

is an indefinite form. You can think of this as being `x*y`

when both x and y are CVX (optimization) variables.

Is your problem convex? If so, how have you proven it? Why isn't CVX accepting my model? READ THIS FIRST!

ouss
(Maîtrise en télécommunications)
April 11, 2017, 5:19pm
3
I am trying to implement an algorithm of an article that is not mine. But in the article, they say that the problem is convex. Plus, when I put U in as a comment, the rest of the algorithm works. I just needed the matrix U = u*u’ to be used in 1 of the constraints.

ouss
(Maîtrise en télécommunications)
April 11, 2017, 5:30pm
4
If not, do you know a function that can produce u from U such as U = u*u’ ? and is it possible to use it with CVX? Thank you

`u'*u`

is fine, `u*u'`

is not fine.

Does the article provide a proof of convexity? If the problem is convex, it may or may not be representable by CVX. Although I know nothing about this paper, I will say that not all claims in all papers are correct.

If it is convex, perhaps there is some rearrangement (reformulation) get it into a form which can be accepted by CVX.

ouss
(Maîtrise en télécommunications)
April 11, 2017, 6:06pm
6
Can I send you the article so you can help me figure out the problem if you have time?

I think it is incumbent on you to read the article and figure it out.