I have implemented a Bender's decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the slave dual LP. As you can see below, the coefficients seem well behaved but I still get warnings like the one highlighted. I have already tried different values for classic parameters like NumericFocus and MarkowitzTol but without success. One such LP that displays this problem can be found here.

  Matrix range     [3e-01, 9e+02]
  Objective range  [1e-02, 9e+02]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e+01, 2e+02]
Warning: very big Kappa = 2.97774e+13, try parameter NumericFocus
  • $\begingroup$ You might want to contact their support (which you probably can also do if you work with other commercial and open source solvers) and give them your problem(s). Usually they are interested if there are problems that look unsuspicious but cause numerical problems. Even if you do not have a commercial license, you still can give it a try. $\endgroup$
    – JakobS
    Sep 14 '19 at 8:15
  • 2
    $\begingroup$ According to CPLEX, the slave dual is unbounded. I see no warnings about kappa values. However, it should be noted that exporting to a text file (such as LP format) can subtly alter coefficients in a way that creates (or possibly masks?) numeric issues. $\endgroup$
    – prubin
    Sep 14 '19 at 19:09

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