For a reasonable sized continuous QP problem, the default Cplex settings indicate problems:
Total time on 1 threads = 0.19 sec.
Solution available but not proven optimal due to numerical difficulties.
This is a matrix balancing problem, where we try to repair economic data matrices after dropping small values, while maintaining some important economic identities.
First thing I tried was to use primal and dual simplex methods, but these turned out not very attractive alternatives (primal simplex took a long time, and dual simplex was infeasible after unscaling). The best option turned out to be using the opfion numericalemphasis. Now it solves fine. Of course I believe that I should not have to do this: Cplex itself should understand better than me that it is in trouble and should try to recover from this in a more intelligent way than I can.