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math_spec.boundedness

Provably unbounded models, named before a solver says a bare unbounded.

A variable that is unbounded on the side its objective term improves toward and appears in no constraint runs to infinity for any data at all. Advice rather than a refusal, because the same shape is what a half-written model looks like.

Which side improves is read off the sign the variable enters the objective with: under minimize a +v term runs down toward lower. Where that sign is not decidable without data — a parameter coefficient, or occurrences of both signs — nothing is claimed.

Sign = Literal['+', '-'] | None module-attribute #

unbounded_notes(spec) #

Name every variable the objective can drive to infinity unopposed.

Expands internally: a piecewise: block holds the variables it names, and does so through the constraints it expands into, so the answer is about the expansion whatever the caller happens to hold.

RETURNS DESCRIPTION
list[Advice]

One note per variable that is unbounded on the side its objective term
list[Advice]

improves toward and named by no constraint.
Source code in src/math_spec/boundedness.py 
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def unbounded_notes(spec: str | Path | dict[str, Any] | Spec) -> list[Advice]:
    """Name every variable the objective can drive to infinity unopposed.

    Expands internally: a ``piecewise:`` block holds the variables it names,
    and does so through the constraints it expands into, so the answer is
    about the expansion whatever the caller happens to hold.

    Returns:
        One note per variable that is unbounded on the side its objective term
        improves toward and named by no constraint.
    """
    schema = expand_piecewise(to_spec(spec))
    if schema.objective is None:
        return []

    ns = Namespace.of(schema)
    objective = expression_of(schema.objective.expression, schema, ns, 'The objective')
    assert not isinstance(objective, ComparisonNode), 'an objective holds no comparison — checked before this runs'

    constrained = {block.variable for block in schema.sos.values()}
    for cname, cdef in schema.constraints.items():
        constrained |= _variables(expression_of(cdef.expression, schema, ns, f"Constraint '{cname}'"))

    signs: dict[str, Sign] = {}
    _walk(objective, '+', signs)

    minimize = schema.objective.sense == 'minimize'
    notes: list[Advice] = []
    for vname, sign in signs.items():
        if sign is None or vname in constrained:
            continue
        side = 'lower' if minimize == (sign == '+') else 'upper'
        if _is_open(schema.variables[vname], side):
            notes.append(
                Advice(
                    'unbounded',
                    vname,
                    f"Variable '{vname}' makes this model unbounded: no constraint names it, and "
                    f'bounds.{side} is {_OPEN[side]}, which is the direction a {sign}{vname} term '
                    f'improves a {schema.objective.sense} objective in. No data can change that, so '
                    f'the solve would answer `unbounded` and name nothing.\n'
                    f'Give it a finite bounds.{side}, or the constraint that was meant to define it.',
                )
            )
    return notes