Status: Solved but cvx_optval = NaN

1

I have encountered an issue with my CVX optimization problem. When I include the constraint b.*(BW/w).*fr >= T;, the solver returns cvx_optval = NaN. However, if I remove this constraint, the problem is solved and cvx_optval has a valid value. Furthermore, when I verify the constraint outside of CVX, it appears to be valid. Could you please advise on how to resolve this issue?
this is my code:
SBS =[1.1485,0.3434,1.6773,0.6964,1.3661];
B=[
1 0 0 0 0
0 0 1 0 0
0 1 0 0 0
0 0 0 1 0
0 0 0 0 1];
w=5;
BSD =[0.0028 0.0010 0.0013 0.0032 0.0019];
NR = 7.9600e-14;
LE = 3.5;
PBS = 39.8107;
b =1;
BW=20;
T =1;
clear cvx_status
clear ZO
clear fr
cvx_begin
clear cvx_status
clear ZO
variable ZO(w,1)
obj1 = (sum(sum(log(1+(SBS’.(BSD’.^LE).ZO./NR)))))./log(2);
minimize -obj1
subject to
ZO >= 0;
ZO <= PBS;
sum(sum(BZO)) <= PBS ;
fr = (log(1+(SBS’.(BSD’.^LE).ZO./NR)))./log(2);
b.(BW/w).*fr >= T;
cvx_end
the output is
Successive approximation method to be employed.
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 41 variables, 10 equality constraints
10 exponentials add 80 variables, 50 equality constraints

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
7/ 7 | 5.454e+00 5.845e+00 0.000e+00 | Solved
8/ 8 | 3.659e+00 1.734e+00 0.000e+00 | Solved
8/ 8 | 1.435e+00 1.668e+00s 0.000e+00 | Solved
8/ 8 | 2.301e-01 1.712e+00s 0.000e+00 | Solved
8/ 8 | 2.350e-02 1.745e+00s 0.000e+00 | Solved
7/ 7 | 3.090e-03 1.726e+00 0.000e+00 | Solved
3/ 4 | 3.823e-04 1.726e+00 0.000e+00 | Solved
3/ 3 | 4.696e-05 1.726e+00 0.000e+00 | Solved
3/ 3 | 5.785e-06 1.726e+00s 0.000e+00 | Solved
3/ 8 | 1.028e-04 2.085e+00 6.941e-11 | Inaccurate/Solved
3/ 4 | 1.270e-05 2.006e+00 1.372e-10 | Inaccurate/Solved
3/ 3 | 5.500e-06 1.893e+00 0.000e+00 | Solved
3/ 3 | 1.927e-05s 1.871e+00s 0.000e+00 | Solved
3/ 8 | 2.328e-05 2.578e+00 5.434e-12 | Inaccurate/Solved
3/ 3 | 2.750e-06 2.159e+00 0.000e+00 | Solved
3/ 3 | 3.453e-07 2.159e+00s 0.000e+00 | Solved

Status: Failed
Optimal value (cvx_optval): NaN

2

The numerical scaling may be bad. NR = 7.9600e-14 might cause havoc numerically. Try to change units in order to get all non-zero input data to be within a small number of orders of magnitude of 1.

Also, if you have Mosek available as solver, use it; otherwise follow the advice in CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .

3

Thank you so much for your help! This solution is helpful