Raise an error when constraints are added to the wrong MILP

[jdemeyer]

sage: p = MixedIntegerLinearProgram(solver="glpk")
sage: q = MixedIntegerLinearProgram(solver="glpk")
sage: q.add_constraint(p[0] <= 1)
---------------------------------------------------------------------------
GLPKError                                 Traceback (most recent call last)
...
GLPKError: glp_set_mat_row: i = 1; len = 1; invalid row length 
Error detected in file glpapi01.c at line 760

Before #19525, this would instead crash Sage. A crash still happens with COIN (#20360).

This ticket is to actually fix the error completely or give a better error message.

And low-level error message with the PPL and InteractiveLP (#20296 ) backends.

The CVX backend silently adds a new variable that is accessible only to the backend:.

sage: sage: default_mip_solver("cvxopt")
sage: sage: p = MixedIntegerLinearProgram()
sage: sage: q = MixedIntegerLinearProgram()
sage: sage: q.add_constraint(p[0] <= 1)
sage: q.number_of_variables()
1

[mkoeppe]

While MIPVariable objects know which MIP they belong to, their "components" gotten by p[0] etc. are elements of LinearFunctionsParent(base_ring), and do not remember their MIP (nor even their name). So with the current design it does not seem possible to catch the error of adding constraints to the wrong MIP. So unfortunately only lower-level error checking, catching out-of-bounds indices, is possible.

[jdemeyer]

Given that p[0] is just a linear function, it would make the most sense if q.add_constraint(p[0] <= 1) would simply work, not give an error message.

[mkoeppe]

No, q has no variables at this point.

[jdemeyer]

Replying to mkoeppe:

No, q has no variables at this point.

That's exactly my point: the variables should be added by q.add_constraint().

[mkoeppe]

I'm not sure that this would be a good interface. It would allow to add variables, but only variables with default settings (continuous, lower bound 0, no upper bound, no name). I think it's better to raise an error, which could help spot programming mistakes -- at least when there's a dimension mismatch between the two problems. This bound checking should be done by the backends -- see #10232.

[jdemeyer]

Replying to mkoeppe:

at least when there's a dimension mismatch between the two problems.

No. It should be always an error, or never an error. If it's only an error "when there's a dimension mismatch between the two problems", that will be more confusing than either extreme.

[mkoeppe]

Then I strongly prefer to always raise an error in this situation. This requires changes to LinearFunction (a class that is I think only used in the context of MixedIntegerLinearProgram), so that it remembers the MIP that it relates to.

The mapping from MIP variables (and their indexed components) to integer indices (designating backend columns) is determined dynamically, adding a backend column when a MIP variable component is accessed. Because of this there's simply no good way to write correct code that interchanges MIP variables between two MixedIntegerLinearPrograms, or to use LinearFunctions directly somehow (without referring to the correct MIP's variables).

[mkoeppe]

Since the crashes are now on separate tickets, I have changed the title of this ticket.

[mkoeppe]

See also #15159, which raises a similar question when q started out as a copy of p.

[mkoeppe]

A solution could be to change LinearFunctionsParent etc. so that it not only has remembers the base_ring but also the MIP.