Hello,

I am trying to solve the linear relaxation of this lp file with CPLEX 12.10 but I get the following error:

CPLEX Error  1258: No LU factorization exists.
ERROR: LoadError: CPLEX Error  1258: No LU factorization exists.​

I do not understand this error and was not able to find an explanation. Do you know what it means?
Is my problem infeasible? (it should not be)
Is it too big?

Thanks in advance.

------------------------------
Zacharie ALES
------------------------------

#DecisionOptimization

I loaded your LP file into the CPLEX 12.10 interactive optimizer and was greeted by almost 6,400 warnings. You have that many variables (z_3,20_ being one of them) that appear in the bounds section of the file (>= 0, <= 1) but not in the objective function or in any constraint. So I'm pretty sure your model is screwed up.

I went ahead and tried to solve it anyway, and did not get the factorization error. CPLEX determined the model to be infeasible, and in particular pointed to variable m_46_. Apparently there is no value of that variable that can satisfy all constraints ... perhaps because some z variables are missing from those constraints?

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Thank you for your answer. I had never used the interactive optimizer. It indeed gives more details.
I cleaned the lp file and there seems to be no more warnings. Here is the link to the cleaned lp file.

The interactive optimizer is now able to solve the lp. Unfortunately I still have the same error when I call CPLEX from Julia
It is surprising that CPLEX is able to solve it in one case but not the other...

If you have any suggestions I am interested.

------------------------------
Zacharie ALES
------------------------------

Original Message:
Sent: Tue December 01, 2020 04:49 PM
From: Paul Rubin
Subject: Error 1258: No LU factorization exists

I loaded your LP file into the CPLEX 12.10 interactive optimizer and was greeted by almost 6,400 warnings. You have that many variables (z_3,20_ being one of them) that appear in the bounds section of the file (>= 0, <= 1) but not in the objective function or in any constraint. So I'm pretty sure your model is screwed up.

I went ahead and tried to solve it anyway, and did not get the factorization error. CPLEX determined the model to be infeasible, and in particular pointed to variable m_46_. Apparently there is no value of that variable that can satisfy all constraints ... perhaps because some z variables are missing from those constraints?

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

When you say the interactive optimizer is able to solve it, you mean it is able to determine that the problem is infeasible, correct? (That's what I get on the cleaned file.)

Try exporting the file as a .sav file rather than a .lp file, and run that through the interactive optimizer. Converting from internal binary representation to text (.lp format) introduces small rounding changes that sometimes make a big difference in how a model solves. If the interactive optimizer can solve the model in the .sav file, then perhaps there is an issue with the Julia interface. If the interactive optimizer has issues with the .sav file, you may have a problem with the model (possibly leading to numerical stability issues). I checked the condition number of the final basis in the interactive optimizer, and it wasn't bad, but perhaps that is courtesy of rounding/truncation going from binary to text (and then back to binary when loading the .lp file).

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Original Message:
Sent: Fri December 04, 2020 11:26 AM
From: Zacharie ALES
Subject: Error 1258: No LU factorization exists

Thank you for your answer. I had never used the interactive optimizer. It indeed gives more details.
I cleaned the lp file and there seems to be no more warnings. Here is the link to the cleaned lp file.

The interactive optimizer is now able to solve the lp. Unfortunately I still have the same error when I call CPLEX from Julia
It is surprising that CPLEX is able to solve it in one case but not the other...

If you have any suggestions I am interested.

------------------------------
Zacharie ALES
------------------------------


Original Message:
Sent: Tue December 01, 2020 04:49 PM
From: Paul Rubin
Subject: Error 1258: No LU factorization exists

I loaded your LP file into the CPLEX 12.10 interactive optimizer and was greeted by almost 6,400 warnings. You have that many variables (z_3,20_ being one of them) that appear in the bounds section of the file (>= 0, <= 1) but not in the objective function or in any constraint. So I'm pretty sure your model is screwed up.

I went ahead and tried to solve it anyway, and did not get the factorization error. CPLEX determined the model to be infeasible, and in particular pointed to variable m_46_. Apparently there is no value of that variable that can satisfy all constraints ... perhaps because some z variables are missing from those constraints?

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Yes I also get that it is infeasible.

Then, I suspect that it may be due to rounding errors. It worked when I rounded a parameter with a precision of 10^-5.
Unfortunately, I have to solve several problems and it does not always work.

I am not sure if it is possible to get a .sav file in Julia.  I will investigate.

Nevertheless, thank you again for your time and help.

------------------------------
Zacharie ALES
------------------------------

Original Message:
Sent: Fri December 04, 2020 11:53 AM
From: Paul Rubin
Subject: Error 1258: No LU factorization exists

When you say the interactive optimizer is able to solve it, you mean it is able to determine that the problem is infeasible, correct? (That's what I get on the cleaned file.)

Try exporting the file as a .sav file rather than a .lp file, and run that through the interactive optimizer. Converting from internal binary representation to text (.lp format) introduces small rounding changes that sometimes make a big difference in how a model solves. If the interactive optimizer can solve the model in the .sav file, then perhaps there is an issue with the Julia interface. If the interactive optimizer has issues with the .sav file, you may have a problem with the model (possibly leading to numerical stability issues). I checked the condition number of the final basis in the interactive optimizer, and it wasn't bad, but perhaps that is courtesy of rounding/truncation going from binary to text (and then back to binary when loading the .lp file).

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------


Original Message:
Sent: Fri December 04, 2020 11:26 AM
From: Zacharie ALES
Subject: Error 1258: No LU factorization exists

Thank you for your answer. I had never used the interactive optimizer. It indeed gives more details.
I cleaned the lp file and there seems to be no more warnings. Here is the link to the cleaned lp file.

The interactive optimizer is now able to solve the lp. Unfortunately I still have the same error when I call CPLEX from Julia
It is surprising that CPLEX is able to solve it in one case but not the other...

If you have any suggestions I am interested.

------------------------------
Zacharie ALES


Original Message:
Sent: Tue December 01, 2020 04:49 PM
From: Paul Rubin
Subject: Error 1258: No LU factorization exists

I loaded your LP file into the CPLEX 12.10 interactive optimizer and was greeted by almost 6,400 warnings. You have that many variables (z_3,20_ being one of them) that appear in the bounds section of the file (>= 0, <= 1) but not in the objective function or in any constraint. So I'm pretty sure your model is screwed up.

I went ahead and tried to solve it anyway, and did not get the factorization error. CPLEX determined the model to be infeasible, and in particular pointed to variable m_46_. Apparently there is no value of that variable that can satisfy all constraints ... perhaps because some z variables are missing from those constraints?

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University