Originally posted by: Falcon_G

Dear all

Attached I put two file called 4.lp and 4.dua

when I solve it using cplex I get

Parallel mode: deterministic, using up to 7 threads for concurrent optimization.

Bound infeasibility column 'ue(13)#3796'.
Presolve - Unbounded or infeasible.
Solution time =    0.00 sec.
Deterministic time = 1.67 ticks  (1671.84 ticks/sec)

but when I dualize the problem (write .dua file) and solve the dual, I get

Parallel mode: deterministic, using up to 7 threads for concurrent optimization.

Tried aggregator 1 time.
LP Presolve eliminated 3618 rows and 1877 columns.
Aggregator did 12 substitutions.
Reduced LP has 220 rows, 211 columns, and 800 nonzeros.

Iteration log . . .
Iteration:     1   Dual objective     =          5842.570372
Reinitializing dual norms . . .

Dual simplex solved model.


Dual simplex - Optimal:  Objective = 9.0485655548e+003
Solution time =    0.02 sec.  Iterations = 44 (0)
Deterministic time = 3.05 ticks  (190.39 ticks/sec)

So, sounds like there is a numerical issues here. Any suggestion to avoid this? I have to solve tens of thousands of LPs in my subproblem and i need to guarantee that this kind of issues will not happen at all.

I have tried to solve the primal problem with all possible lpmethods in the interactive shell with no avail. Modifying the tolerances also did not solve the problem.

regards,

Shahin

Originally posted by: T_O

If you really need to guarantee this, you will have to use solvers based on exact arithmetic.

Any solver based on floating point arithmetic is by design not able to solve every given LP correctly. Also remember that for CPLEX, it is perfectly ok that a problem is both feasible and infeasible!

Best regards,
Thomas

Originally posted by: Falcon_G

well, I was rather seeking a constructive comment a bit more mature.

Maybe the my question was not clear enough.

Originally posted by: T_O

I am sorry, if I am too unexperienced.

Your problem (4.lp, which might already contain rounded values) is umbounded, but you have very small objective coefficients like 1.11022302462516 · 10^-16. So it might be difficult for simplex algorithms to detect unboundedness. For the presolver, this might be easier. You should avoid such small values.

Best regards,
Thomas