# Constraints

## Types

MathOptInterface.ConstraintIndexType
ConstraintIndex{F, S}

A type-safe wrapper for Int64 for use in referencing F-in-S constraints in a model. The parameter F is the type of the function in the constraint, and the parameter S is the type of set in the constraint. To allow for deletion, indices need not be consecutive. Indices within a constraint type (i.e. F-in-S) must be unique, but non-unique indices across different constraint types are allowed. If F is VariableIndex then the index is equal to the index of the variable. That is for an index::ConstraintIndex{VariableIndex}, we always have

index.value == MOI.get(model, MOI.ConstraintFunction(), index).value
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## Functions

MathOptInterface.is_validMethod
is_valid(model::ModelLike, index::Index)::Bool

Return a Bool indicating whether this index refers to a valid object in the model model.

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MathOptInterface.add_constraintFunction
add_constraint(model::ModelLike, func::F, set::S)::ConstraintIndex{F,S} where {F,S}

Add the constraint $f(x) \in \mathcal{S}$ where $f$ is defined by func, and $\mathcal{S}$ is defined by set.

add_constraint(model::ModelLike, v::VariableIndex, set::S)::ConstraintIndex{VariableIndex,S} where {S}
add_constraint(model::ModelLike, vec::Vector{VariableIndex}, set::S)::ConstraintIndex{VectorOfVariables,S} where {S}

Add the constraint $v \in \mathcal{S}$ where $v$ is the variable (or vector of variables) referenced by v and $\mathcal{S}$ is defined by set.

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MathOptInterface.add_constraintsFunction
add_constraints(model::ModelLike, funcs::Vector{F}, sets::Vector{S})::Vector{ConstraintIndex{F,S}} where {F,S}

Add the set of constraints specified by each function-set pair in funcs and sets. F and S should be concrete types. This call is equivalent to add_constraint.(model, funcs, sets) but may be more efficient.

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MathOptInterface.transformFunction

Transform Constraint Set

transform(model::ModelLike, c::ConstraintIndex{F,S1}, newset::S2)::ConstraintIndex{F,S2}

Replace the set in constraint c with newset. The constraint index c will no longer be valid, and the function returns a new constraint index with the correct type.

Solvers may only support a subset of constraint transforms that they perform efficiently (for example, changing from a LessThan to GreaterThan set). In addition, set modification (where S1 = S2) should be performed via the modify function.

Typically, the user should delete the constraint and add a new one.

Examples

If c is a ConstraintIndex{ScalarAffineFunction{Float64},LessThan{Float64}},

c2 = transform(model, c, GreaterThan(0.0))
transform(model, c, LessThan(0.0)) # errors
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MathOptInterface.supports_constraintFunction
supports_constraint(
model::ModelLike,
::Type{F},
::Type{S},
)::Bool where {F<:AbstractFunction,S<:AbstractSet}

Return a Bool indicating whether model supports F-in-S constraints, that is, copy_to(model, src) does not throw UnsupportedConstraint when src contains F-in-S constraints. If F-in-S constraints are only not supported in specific circumstances, e.g. F-in-S constraints cannot be combined with another type of constraint, it should still return true.

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MOI.supports_constraint(
BT::Type{<:AbstractBridge},
F::Type{<:MOI.AbstractFunction},
S::Type{<:MOI.AbstractSet},
)::Bool

Return a Bool indicating whether the bridges of type BT support bridging F-in-S constraints.

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## Attributes

MathOptInterface.ConstraintNameType
ConstraintName()

A constraint attribute for a string identifying the constraint.

It is valid for constraints variables to have the same name; however, constraints with duplicate names cannot be looked up using get, regardless of whether they have the same F-in-S type.

ConstraintName has a default value of "" if not set.

Notes

You should not implement ConstraintName for VariableIndex constraints.

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MathOptInterface.ConstraintPrimalType
ConstraintPrimal(result_index::Int = 1)

A constraint attribute for the assignment to some constraint's primal value(s) in result result_index.

If the constraint is f(x) in S, then in most cases the ConstraintPrimal is the value of f, evaluated at the correspondng VariablePrimal solution.

However, some conic solvers reformulate b - Ax in S to s = b - Ax, s in S. These solvers may return the value of s for ConstraintPrimal, rather than b - Ax. (Although these are constrained by an equality constraint, due to numerical tolerances they may not be identical.)

If the solver does not have a primal value for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintPrimal attribute.

If result_index is omitted, it is 1 by default. See ResultCount for information on how the results are ordered.

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MathOptInterface.ConstraintDualType
ConstraintDual(result_index::Int = 1)

A constraint attribute for the assignment to some constraint's dual value(s) in result result_index. If result_index is omitted, it is 1 by default.

If the solver does not have a dual value for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a primal solution is available), the result is undefined. Users should first check DualStatus before accessing the ConstraintDual attribute.

See ResultCount for information on how the results are ordered.

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MathOptInterface.ConstraintBasisStatusType
ConstraintBasisStatus(result_index::Int = 1)

A constraint attribute for the BasisStatusCode of some constraint in result result_index, with respect to an available optimal solution basis. If result_index is omitted, it is 1 by default.

If the solver does not have a basis statue for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintBasisStatus attribute.

See ResultCount for information on how the results are ordered.

Notes

For the basis status of a variable, query VariableBasisStatus.

ConstraintBasisStatus does not apply to VariableIndex constraints. You can infer the basis status of a VariableIndex constraint by looking at the result of VariableBasisStatus.

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MathOptInterface.BasisStatusCodeType
BasisStatusCode

An Enum of possible values for the ConstraintBasisStatus and VariableBasisStatus attributes, explaining the status of a given element with respect to an optimal solution basis.

Possible values are:

• BASIC: element is in the basis
• NONBASIC: element is not in the basis
• NONBASIC_AT_LOWER: element is not in the basis and is at its lower bound
• NONBASIC_AT_UPPER: element is not in the basis and is at its upper bound
• SUPER_BASIC: element is not in the basis but is also not at one of its bounds

Notes

• NONBASIC_AT_LOWER and NONBASIC_AT_UPPER should be used only for constraints with the Interval set. In this case, they are necessary to distinguish which side of the constraint is active. One-sided constraints (e.g., LessThan and GreaterThan) should use NONBASIC instead of the NONBASIC_AT_* values. This restriction does not apply to VariableBasisStatus, which should return NONBASIC_AT_* regardless of whether the alternative bound exists.

• In linear programs, SUPER_BASIC occurs when a variable with no bounds is not in the basis.

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MathOptInterface.ConstraintFunctionType
ConstraintFunction()

A constraint attribute for the AbstractFunction object used to define the constraint. It is guaranteed to be equivalent but not necessarily identical to the function provided by the user.

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MathOptInterface.CanonicalConstraintFunctionType
CanonicalConstraintFunction()

A constraint attribute for a canonical representation of the AbstractFunction object used to define the constraint. Getting this attribute is guaranteed to return a function that is equivalent but not necessarily identical to the function provided by the user.

By default, MOI.get(model, MOI.CanonicalConstraintFunction(), ci) fallbacks to MOI.Utilities.canonical(MOI.get(model, MOI.ConstraintFunction(), ci)). However, if model knows that the constraint function is canonical then it can implement a specialized method that directly return the function without calling Utilities.canonical. Therefore, the value returned cannot be assumed to be a copy of the function stored in model. Moreover, Utilities.Model checks with Utilities.is_canonical whether the function stored internally is already canonical and if it's the case, then it returns the function stored internally instead of a copy.

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