[FileFormats] the MPS and LP writers mishandle the constant of a constraint function #3109

import MathOptInterface as MOI
for Model in (MOI.FileFormats.MPS.Model, MOI.FileFormats.LP.Model)
    model = Model()
    MOI.Utilities.loadfromstring!(
        model,
        """
        variables: x
        minobjective: 1.0 * x
        x >= 0.0
        c: 2.0 * x + -5.0 >= 0.0
        """,
    )
    print(sprint(write, model))
end

The MPS file has rhs c 0, so it says 2x >= 0 instead of 2x >= 5, and MOI reads it back that way. JuMP users can hit this by converting an LP file containing c: 2 x - 5 >= 0 to MPS with read_from_file and write_to_file.

The LP file has c: -5 + 2 x >= 0. That is valid in the grammar in the LP docs, and MOI reads it back correctly, but Gurobi reads 5 as a new variable and HiGHS 1.15.1 drops the -5, so both return an optimum of 0 instead of 2.5. HiGHS latest also ignores it, with a warning.

Indicators do the same: [z, 2x - 5] in Indicator{ACTIVATE_ON_ONE}(GreaterThan(0.0)) writes rhs c 0 in MPS and c: z = 1 -> -5 + 2 x >= 0 in LP.

For MPS, which has no field for a row constant, the options I can see:

1. Record each nonzero constant while COLUMNS is collected (the writer already gets every function there), and subtract it in write_rhs. This passes one more argument through the _collect_* and _write_rhs calls.
2. Get the function again in _write_rhs and subtract its constant. This is a smaller change, but it copies the constraint functions again.
3. Throw an error when a function has a nonzero constant.

For LP:

1. Move the constant to the right-hand side with MOI.Utilities.normalize_constant. This changes the expected output of three existing tests, for example c6: -1.4 + 1.3 x >= -0.1 becomes c6: 1.3 x >= 1.2999999999999998.
2. Keep the output and document it in the "Differences" section of the LP docs.

I have prototypes of option 1 for both, with tests. Which would you prefer?