Originally posted by: Katzmann

Hello everyone,
I am using Cplex optimizer to solve a quadratic problem. After only 12 iterations with the barrier method Cplex stops and returns the non-optimal solution.
The parameter barrier.iteration is equal to 2100000000, so it should continue.

If I use the dual simplex method the solution is found.

Any help especially, where I could find the stopping criterion used, would be greatly apprechiated.
Thanks,
Jens
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Originally posted by: SystemAdmin

Why do you think it is not optimal? The difference in the objective values of primal and dual problems seems to be very small after 12 iterations. So I think it stopped not because it reached the iteration limit but it dropped within the gap of abs|obj. of dual - obj. primal|. For the setting parameters for stopping criteria, you could refer to the manual CPLEXX_Xmannuals->ILOG CPLEX Parameters->Topical list of parameters->Barrier->convergence tolerance for LP and QP problems
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Originally posted by: SystemAdmin

I don't solve QPs very often (i.e., almost never), so take what I say with a grain of salt. The gap in the last iteration does seem a bit large (on the order of 10^-5) relative to the default convergence criterion (which I assume you did not change), and the final status does say "Non-optimal". What happens if you set the crossover algorithm parameter to dual simplex? (AFAIK crossover is turned off by default, and there's no indication of it occurring in your log file.) You might also see what happens if you turn on the numerical precision emphasis switch.

Although there's no explicit indication of it in the output, I wonder if CPLEX encountered what would amount to a step size of zero trying to do a 13th iteration?

/Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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Originally posted by: EdKlotz

> Paul Rubin wrote:
> I don't solve QPs very often (i.e., almost never), so take what I say with a grain of salt. The gap in the last iteration does seem a bit large (on the order of 10^-5) relative to the default convergence criterion (which I assume you did not change), and the final status does say "Non-optimal". What happens if you set the crossover algorithm parameter to dual simplex? (AFAIK crossover is turned off by default, and there's no indication of it occurring in your log file.) You might also see what happens if you turn on the numerical precision emphasis switch.
>
> Although there's no explicit indication of it in the output, I wonder if CPLEX encountered what would amount to a step size of zero trying to do a 13th iteration?
>
> /Paul
>
> Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
In addition to turning on numerical emphasis, see what happens if you increase the barrier convergence tolerance from its default of 1e-8 to a slightly larger value, such as 1e-6. It looks like the barrier algorithm almost converged, but could not make additional improvements in the
objective, so that the normalized duality gap mentioned above didn't quite get below the convergence
tolerance. If that is what happened, then increasing the convergence tolerance will result
in a conclusion of optimality.

However, that does not necessarily mean that increasing the optimality tolerance provides the best resolution to your issue. Can you upload a SAV file of the model?

Ed
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Originally posted by: Katzmann

Thanks to all of you for your help.

The Status is 'non-optimal', even though the solution provided is quite close to the optimal solution.

Switching the solver actually helped. The problem could be solved by the Dual Simplex.

The problem was also solved by switching the parameter barrier.convergetol to 1e-6 as EdKlotz suggested. It then performed a 13th iteration with the Dual Inf small enough for the solution to count as optimal.

The problem seemed to be due to the problem itself being rather unstable. In fact the size of the coefficients ranged from 10**-3 up to 10**4.
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