[Help-glpk] basis matrix is singular, but not in the saved model

[Mark Gritter]

I am using GLPK to solve some game-theory problems with dense matrices
(as I have asked about before.)  Andrew's suggestion to use column
generation has been very useful (thank you!)

In my current program I got the following error while running
lpx_simplex on the main LP model:

* 44250:   objval =   1.482023718e+00   infeas =   9.060097142e-14 (0)
* 44300:   objval =   1.481789163e+00   infeas =   9.819968853e-16 (0)
* 44350:   objval =   1.481729328e+00   infeas =   6.997407302e-14 (0)
spx_invert: the basis matrix is singular
spx_simplex: numerical problems with basis matrix
spx_simplex: sorry, basis recovery procedure not implemented yet

However, when I run the saved model through glpsol it arrives at a solution:

lpx_read_cpxlp: reading problem data from `test.cplex'...
lpx_read_cpxlp: 1687 rows, 2248 columns, 1898434 non-zeros
lpx_read_cpxlp: 949119 lines were read
lpx_write_mps: writing problem data to `test.mps'...
lpx_simplex: original LP has 1687 rows, 2248 columns, 1898434 non-zeros
lpx_simplex: presolved LP has 1687 rows, 2248 columns, 1898434 non-zeros
lpx_adv_basis: size of triangular part = 1687
     0:   objval =   0.000000000e+00   infeas =   1.000000000e+00 (0)
   200:   objval =   1.344510660e+00   infeas =   3.297820208e-01 (0)
   400:   objval =   1.881226167e+00   infeas =   1.941659565e-01 (0)
...
*  2400:   objval =   1.481966312e+00   infeas =   7.559774601e-14 (0)
*  2600:   objval =   1.481709975e+00   infeas =   0.000000000e+00 (0)
*  2648:   objval =   1.481704489e+00   infeas =   2.057120297e-17 (0)
OPTIMAL SOLUTION FOUND

Right now my loop works something like this:

1. Save the model to file
2. Solve restricted problem with lpx_simplex
3. Look for additional rows (first-player strategies that improve his
score).  If found, add them to the model and go back to step #1.
4. Look for additional columns (second-player strategies) with
negative reduced cost.  If found, add them to the model and repeat
step #1.

Should I reset the basis before running the simplex method again?
Could I recover from this error by resetting the basis and rerunning
lpx_simplex?

Thanks,
Mark