SCA log leads to fail

1

Dear all,

For the following optimization problem

cvx_begin 
        variable p(K,1);
        obj = 0;
        for k=1:K
            obj = obj + log(1 + v(k)*p(k));
        end
        maximize( obj )
        subject to
            const1'*p <= m;
            p>0;
cvx_end

where v and const1 are vectors of size K with positive entries. Moreover, m is also positive. I get the following result:

Successive approximation method to be employed.
SDPT3 will be called several times to refine the solution.
Original size: 13 variables, 7 equality constraints
3 exponentials add 24 variables, 15 equality constraints

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
3/ 3 | 8.000e+00 9.264e+01 0.000e+00 | Inaccurate/Solved
3/ 3 | 8.000e+00s 2.323e+01 0.000e+00 | Solved
3/ 3 | 6.188e+00 2.615e+00 0.000e+00 | Failed
3/ 3 | 2.321e+00 2.967e-01 0.000e+00 | Failed
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed

Status: Failed
Optimal value (cvx_optval): NaN

I am using CVX, version 2.0 (beta) and MATLAB version: 8.0 (R2012b).

Do you have any suggestion of how can I solve this problem?

2

Try SeDuMi or ECOS. If you MOSEK avaialble, try using it.

3

SeDuMi does not show any fail.

Thanks,

MA