No-product rule

Nonconvex
1

I have a fraction constraints:

 cvx_begin
   variable X(3,3) hermitian;
   variable t(2);
                 
   q1 = trace(X*R1);
   q2 = trace(X*R2);
                       
   j1 = trace(real(X*M1))+1;
   j2 = trace(real(X*M2))+1;
                  
   maximize  geo_mean(t,1,W)
   subject to
       %% this what i want to do: q1/j1 >= t(1) &   q2/j2 >= t(2)
       q1 >= t(1)*j1
       q2 >= t(2)*j2

It seems that the two last two lines violate the no-product rule at the right-hand side

Where R1,R2,M1,M2, and W are constants.

How can i write this constraint in CVX?

The Error:

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 max_min_assump1_plus_WSRM_02 (line 319)
                       q1 >= t(1)*j1

Edited Part:

The original model was:

$$ maximize \sum W_i log (q_i/j_i) \quad , i =1,2 $$
$$ s.t \quad some \quad constraints $$

which could be transformed to:

$$ maximize \prod (q_i/j_i)^{W_i} \quad , i =1,2 $$
$$ s.t \quad some \quad constraints $$

Then it can be transformed according to one of Boyd papers (Qos and Fairness Constrained convex optimization of resource allocation) to:

$$ maximize \prod (t_i)^{W_i} \quad , i =1,2 $$
$$ s.t \quad some \quad constraints $$
$$ \quad q_i/j_i \ge t_i $$

my problem now is with this constraint

2

Is your model convex? It does not appear so.

3

i added some details on the original problem in the edited section

4

I am afraid I cannot spend time reading a paper to see how the problem is transformed to convex form. All I can tell you is that, as written, it is not convex, and not compatible with CVX.