[Numerical] Barrier method fails on numerically difficult LP instance that solved by other cuOpt methods

[alexander-popkov]

Describe the bug
Running cuopt_cli with barrier method (method=3) on a big MPS model fails reproducibly with a numerical error during barrier search direction computation.

The model is numerically difficult, and cuOpt reports a very large coefficient range. However, the same instance is handled successfully by other methods within cuOpt, as well as by alternative solvers. This suggests a barrier-specific robustness issue rather than a general model validity issue.

Environment

• cuOpt version: 26.2.0
• git hash: f73da24d
• CUDA version: 12.9
• GPU: NVIDIA H200
• CPU: Intel(R) Xeon(R) Platinum 8480+
• RAM: 427.29 GiB

Problem summary

• LP instance
• 424118 constraints
• 1367797 variables
• 4512958 nonzeros

Coefficient ranges reported by cuOpt:

• Objective coefficients: [1e-03, 8e+05]
• Constraint matrix coefficients: [1e-18, 8e+05]
• RHS / bounds: [5e-12, 3e+07]
• Variable bounds: [4e-15, 4e+07]

Reproduction

1. Unzip the attached file. It is double-compressed to meet github requirements.
2. Run cuopt_cli --method 3 big_lp_obf.mps

Observed behavior
The barrier solve terminates with:

Search direction computation failed
Barrier Solve status A numerical error was encountered.

cuOpt also reports that the post-solved solution violates constraints.

Expected behavior
Barrier should either solve this instance successfully or fail more robustly on a model that is solvable by other cuOpt methods.

Attachments

• Full solver log

Notes
I understand that the model has serious numerical issues. However, since it is solved by other cuOpt methods and by other solvers, I believe this is a barrier-specific robustness bug.

big_lp_obf.log

[anandhkb]

@mlubin @chris-maes @bbozkaya @afender for viz

[chris-maes]

Unfortunately, I think this falls under expected behavior. We are failing as robustly as we can here.

Not every method can solve every problem. Barrier can struggle on numerically ill-conditioned problems. The error "search direction computation failed" simply means the linear system solve had such large residual that the solve could not continue.

We can add your problem to our test sets and see if we can improve upon it. But as you note, the large range of coefficients in this problem may it numerically challenging.

[chris-maes]

@anandhkb could you mark this ticket as "Numerical Issue" instead of bug? Thank you!