Originally posted by: SystemAdmin

Hello.
Could you please tell me why do I obtain these results with CPLEX:
- I get an objective value of 3.3621572725e+000 for the attached LP formulator_out_CPLEX_avg_with_constraint_equal_1.lp .
- however, when I remove from the LP the constraint sum of all variables = 1 (this constraint is just before the Bounds keyword), CPLEX finds an optimal solution with objective value of 0.0.

I ask because I was assuming that since I have a maximization problem and the original LP is more constrained than the one without the sum=1 constraint, the less constraint LP will result in a >= objective value w.r.t the original LP.

It seems that lp_solve has the same behavior.

Thank you,
Alex
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Originally posted by: SystemAdmin

Your problem is ill-conditioned. (In fact, it may be the poster child for ill-conditioned problems.) I can reproduce your objective values here (with CPLEX 9.1). For the problem with the last constraint included, the condition number of the basis matrix is 284929, which is scary enough. With the last constraint removed, though, I get a condition number around 3.5 x 10^10 if I delete and resolve after solving the full problem (3.4 x 10^9 if I read the problem fresh, delete the constraint and then solve).

So the zero solution is utterly untrustworthy, and I'm not sure just how accurate the non-zero solution is.

/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: SystemAdmin

Hello.

With CPLEX 11.1.1 I obtain the following condition numbers (I use the following CPLEX interactive optimizer command: "display solution kappa" OR I can use "disp sol quality"):
- for the original LP (with sum of all vars = 1):
Condition number of scaled basis = 8.7e+004
- for the LP that does not have sum of all vars = 1:
Condition number of scaled basis = 1.7e+009

Are these the right condition numbers?

Out of curiosity, is there anything I can do to obtain the optimal solution to the LP with condition number = 1.7e+009. I tried:
set emphasis numerical yes
OR
set feasopt tolerance 1e-3
set simplex tolerances feasibility 1e-3
set network tolerances feasibility 1e-3
In the CPLEX manual it is written: "Check the basis condition number, as explained in Measuring problem sensitivity with basis condition number. If the condition number is fairly low (for example, as little as 1e5 or less), then you can be confident about the solution. If the condition number is high, or if reducing
tolerance does not help, then you must revise the model because the current model may be too ill-conditioned to produce a numerically reliable result."

Could you please point me to some good reference (book or paper) that talks about condition number. So far, I found http://en.wikipedia.org/wiki/Condition_number.

Thank you very much,
Alex
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Originally posted by: SystemAdmin

In your problem file I note data with 6 digits, e.g. 0.016393 and 0.054962 . I presume these to be truncations of the intended coefficients, perhaps generated in a program using 32-bit floating arithmetic (e.g. "float") rather than 64-bit ("double"). The first thing I would do is re-generate using the latter.

If you tighten the simplex feasibility tolerance to its minimum value of 1e-9, the primal simplex and dual simplex method both terminate with a status of "infeasible" on your present formulation, having a bound infeasibility in the neighborhood of 1e-7, which I imagine is not the expected outcome, and may be due to the truncated input data. As a simple example, constraints like 0.333333 x + 0.333333 y + 0.333333 z = 1 can be expected to give unwanted results in conjunction with other constraints, while longer representations of the intended data (1/3) become more robust.
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Originally posted by: Bo7

I'm asking if the teaching edition for university professors is gonna be unlimited and free.
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