Hi Joachim,I often encounter this problem of 'singular KKT matrix' which disappears if I find a proper rescaling of the problem.Do you have any rule of thumb of how to determine the rescaling factor?S.
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Thank you for your answer! Apparently, I fall in the case
* Ax=b where a few b[k] are very large, or a few A[k,j] are very large.
The re-scaling is not always successful. I am working on a nice reformulation as a SOCP problem, but I don't know if I will have similar issues. Is it likely to be more robust?Best,Sylvain
[ 0.00e+00 0.00e+00 -1.00e+00] [ 1.30e+01 -3.00e+00 0.00e+00] [ 1.20e+01 -1.20e+01 0.00e+00]
[ 0.00e+00 1.30e+01 1.20e+01] [ 0.00e+00 -3.00e+00 -1.20e+01] [-1.00e+00 0.00e+00 0.00e+00]
The next release of CVXOPT will address some known issues with Numpy compatibility, but we will continue to use a column-major input format in cvxopt.matrix. This is consistent with how the data is actually stored. Numpy arrays can be stored as either row-major or column-major, but the array routine assumes row-major input regardless of how you decide to store the data.
Martin
pcost dcost gap pres dres k/t 0: -1.0000e+00 -1.0000e+00 2e+02 4e+00 1e+00 1e+00 1: -4.5232e+00 -4.5713e+00 1e+01 4e-01 1e-01 5e-02 2: -2.7795e+00 -2.7572e+00 2e+00 1e-01 3e-02 4e-02 3: -2.5992e+00 -2.5529e+00 2e+00 9e-02 3e-02 7e-02 4: -2.3703e+00 -2.3471e+00 9e-01 3e-02 9e-03 3e-02 5: -2.1825e+00 -2.1728e+00 2e-01 7e-03 2e-03 1e-02 6: -2.1055e+00 -2.0964e+00 2e-01 4e-03 1e-03 1e-02 7: -2.0806e+00 -2.0761e+00 1e-01 2e-03 4e-04 5e-03 8: -2.0391e+00 -2.0354e+00 7e-02 5e-04 1e-04 4e-03 9: -2.0244e+00 -2.0226e+00 3e-02 2e-04 4e-05 2e-03 10: -2.0198e+00 -2.0180e+00 3e-02 1e-04 4e-05 2e-03 11: -2.0117e+00 -2.0109e+00 1e-02 3e-05 9e-06 8e-04 12: -2.0094e+00 -2.0085e+00 2e-02 3e-05 8e-06 9e-04 13: -2.0052e+00 -2.0049e+00 5e-03 7e-06 2e-06 4e-04 14: -2.0035e+00 -2.0032e+00 6e-03 4e-06 1e-06 3e-04 15: -2.0022e+00 -2.0021e+00 2e-03 1e-06 3e-07 2e-04 16: -2.0018e+00 -2.0016e+00 3e-03 1e-06 3e-07 2e-04 17: -2.0011e+00 -2.0010e+00 1e-03 3e-07 9e-08 8e-05 18: -2.0010e+00 -2.0009e+00 2e-03 3e-07 9e-08 9e-05 19: -2.0006e+00 -2.0006e+00 6e-04 9e-08 3e-08 4e-05 20: -2.0005e+00 -2.0004e+00 9e-04 9e-08 2e-08 4e-05 21: -2.0003e+00 -2.0003e+00 3e-04 2e-08 6e-09 2e-05 22: -2.0003e+00 -2.0002e+00 4e-04 2e-08 7e-07 2e-05 23: -2.0002e+00 -2.0002e+00 2e-04 7e-09 4e-07 1e-05 24: -2.0001e+00 -2.0001e+00 2e-04 6e-09 4e-06 1e-05 Terminated (singular KKT matrix).