It is interesting to see how Gurobi recovers from numerical trouble in a difficult (dense) LP, when using the primal simplex algorithm:
Iteration Objective Primal Inf. Dual Inf. Time
0 1.6911927e+08 0.000000e+00 1.779242e+04 1s
9864 1.4022077e+06 0.000000e+00 6.819017e+01 5s
Warning: 1 variables dropped from basis
Warning: switch to quad precision
13988 1.3343358e+06 0.000000e+00 1.064917e+02 10s
14726 1.3299619e+06 0.000000e+00 0.000000e+00 13s
Apparently it switches to quadruple precision. Those are REAL*16 numbers, yielding approx. 34 decimal digits of precision. I don’t think I have ever seen this capability in other solvers.
wow, that is cool.
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