Status: Infeasible

1

the following code works fine and gives me the optimal solution for the given input, but when I change m = 1 and r = [11 6] the problem becomes infeasible which is not!!!
any idea what am I missing here?

r = [11 6; 11 6];
m = 2;    % Stations
n = 2;     % APs
cvx_begin
    variable tp(m,n);
    f1 = sum(log(sum(tp(1:m,1:n).*r))); 
    maximize (f1)
    subject to
        0 <= tp <= 1;
        sum(tp,2) <= 1;
        sum(tp,1) == 1;
cvx_end
2

See Edit below: Otherwise, i have preserved my original post for thread context.

Using SeDuMi in CVX Build 2.1, m=2,r=[11 6;11 6]; worked for me, and m=1,r=[11 6]; incorrectly reported infeasible.

Using SDPT3, both cases were successfully solved.

Moreover, success or lack thereof was unaffected when I removed log from the objective function (f1), thereby making the problem into an LP. So the problem is not with CVX’s successive approximation method for dealing with log.

It looks to me like a bug somewhere in CVX or SeDuMi. It seems like the combination m=1, n > 1 is not being handled properly. We will have to wait to see what @mcg says.

For now, i think you can specify SDPT3 as the solver. Or you can try other solvers if you have them available.

Edit: Sorry, it was late and I was tired. Looking back at my runs, I did not have any successful (not reported infeasible) runs with m = 1 and n > 1 using SeDuMi or SDPT3, with or without the log.

3

Thanks. I took your advice and tried SDP3 but still it gives me infeasible status. is my code right?

cvx_solver SDPT3
r = [11 6];
m = 1;     % Stations
n = 2;     % APs
cvx_begin
    variable tp(m,n);
    f1 = sum(log(sum(tp(1:m,1:n).*r))); 
    maximize (f1)
    subject to
        0 <= tp <= 1;
        sum(tp,2) <= 1;
        sum(tp,1) == 1;
cvx_end

>> cvx_test3
 
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: 8 variables, 1 equality constraints
   1 exponentials add 8 variables, 5 equality constraints
-----------------------------------------------------------------
 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
4

Sorry, it was late and I was tired. Looking back at my runs, I did not have any successful (not reported infeasible) runs with m = 1 and n > 1 using SeDuMi or SDPT3, with or without the log.

5

any feedback from @mcg?