Presolve error and small values

[jajhall]

I'm experimenting with two related (proprietary) LPs, for which the solutions when running presolve are incorrect. I've verified that they have large dual infeasibilities. With presolve off, it's OK. Without the MPS files, I know that this is useless to you for debugging purposes, but I thought that I'd raise the issue.

The models also have a very large number of tiny values: more than 30% are below 1e-11 in absolute value. Such small values are ignored in other solvers and, in this case, contribute meaningfully to the computational cost of cuPDLPx. Note that I've just created MPS files for the LPs with these small values removed, and the presolve error disappears.

In passing, the date "2025" still appears in the logging for v0.2.5

[ZedongPeng]

Hi @jajhall — thanks a lot for reporting this, and for the careful triage.

Such small values are ignored in other solvers

Just to make sure I understand: do you mean the tiny coefficients are dropped at the MPS parsing/reading stage (i.e., treated as structural zeros), or are they kept in the model but ignored later (e.g., by presolve/scaling/numerics)?

Since you work on HiGHS, I’d be interested in how HiGHS handles this in practice (typical threshold, and whether it’s applied in the reader or downstream). That would help us decide where to implement a similar safeguard in cuPDLPx.

[jajhall]

Yes, the tiny values are dropped, and are not retained as structural zeros.

Since HiGHS models can be passed in code, or read using more than one file format, the filtering is done after reading from a file.

• Gurobi appears to have a tolerance of 1e-13, that is not settable, and may be as large as 1e-9
• Xpress has MATRIXTOL of 1e-9
• HiGHS has the settable option small_matrix_value with a default value of 1e-9