# Extending JuMP

## Extending MOI

See the bridge section in the MOI manual.

JuMP.add_bridgeFunction
 add_bridge(model::Model,
BridgeType::Type{<:MOI.Bridges.AbstractBridge})

Add BridgeType to the list of bridges that can be used to transform unsupported constraints into an equivalent formulation using only constraints supported by the optimizer.

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JuMP.BridgeableConstraintType
struct BridgeableConstraint{C, B} <: AbstractConstraint
constraint::C
bridge_type::B
end

Constraint constraint that can be bridged by the bridge of type bridge_type. Adding this constraint to a model is equivalent to

add_bridge(model, bridge_type)
add_constraint(model, constraint)

Examples

Given a new scalar set type CustomSet with a bridge CustomBridge that can bridge F-in-CustomSet constraints, when the user does

model = Model()
@variable(model, x)
@constraint(model, x + 1 in CustomSet())
optimize!(model)

with an optimizer that does not support F-in-CustomSet constraints, the constraint will not be bridged unless he manually calls add_bridge(model, CustomBridge). In order to automatically add the CustomBridge to any model to which an F-in-CustomSet is added, simply add the following method:

function JuMP.build_constraint(_error::Function, func::AbstractJuMPScalar,
set::CustomSet)
constraint = ScalarConstraint(func, set)
return JuMP.BridgeableConstraint(constraint, CustomBridge)
end

Note

JuMP extensions should extend JuMP.build_constraint only if they also defined CustomSet, for three reasons:

1. It is problematic if multiple extensions overload the same JuMP method.
2. A missing method will not inform the users that they forgot to load the extension module defining the build_constraint method.
3. Defining a method where neither the function nor any of the argument types are defined in the package is called type piracy and is discouraged in the Julia style guide.
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## Extending JuMP macros

In order to provide a convenient syntax for the user to create variables, constraints or set the objective of a JuMP extension, it might be required to use macros similar to @variable, @constraint and @objective. It is recommended to first check whether it is possible to extend one of these three macros before creating a new one so as to leverage all their features and provide a more consistent interface to the user.

### Extending the @constraint macro

The @constraint macro always calls the same three functions:

Adding methods to these functions is the recommended way to extend the @constraint macro.

#### Adding parse_constraint methods

JuMP.sense_to_setFunction
sense_to_set(_error::Function, ::Val{sense_symbol})

Converts a sense symbol to a set set such that @constraint(model, func sense_symbol 0) is equivalent to @constraint(model, func in set) for any func::AbstractJuMPScalar.

Example

Once a custom set is defined you can directly create a JuMP constraint with it:

julia> struct CustomSet{T} <: MOI.AbstractScalarSet
value::T
end

julia> Base.copy(x::CustomSet) = CustomSet(x.value)

julia> model = Model();

julia> @variable(model, x)
x

julia> cref = @constraint(model, x in CustomSet(1.0))
x ∈ CustomSet{Float64}(1.0)

However, there might be an appropriate sign that could be used in order to provide a more convenient syntax:

julia> JuMP.sense_to_set(::Function, ::Val{:⊰}) = CustomSet(0.0)

julia> MOIU.shift_constant(set::CustomSet, value) = CustomSet(set.value + value)

julia> cref = @constraint(model, x ⊰ 1)
x ∈ CustomSet{Float64}(1.0)

Note that the whole function is first moved to the right-hand side, then the sign is transformed into a set with zero constant and finally the constant is moved to the set with MOIU.shift_constant.

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#### Adding build_constraint methods

There are typically two choices when creating a build_constraint method, either return an AbstractConstraint already supported by the model, i.e. ScalarConstraint or VectorConstraint, or a custom AbstractConstraint with a corresponding add_constraint method (see Adding add_constraint methods).

JuMP.build_constraintFunction
build_constraint(_error::Function, Q::Symmetric{V, M},
::PSDCone) where {V <: AbstractJuMPScalar,
M <: AbstractMatrix{V}}

Return a VectorConstraint of shape SymmetricMatrixShape constraining the matrix Q to be positive semidefinite.

This function is used by the @constraint macros as follows:

@constraint(model, Symmetric(Q) in PSDCone())

The form above is usually used when the entries of Q are affine or quadratic expressions, but it can also be used when the entries are variables to get the reference of the semidefinite constraint, e.g.,

@variable model Q[1:2,1:2] Symmetric
# The type of Q is Symmetric{VariableRef, Matrix{VariableRef}}
var_psd = @constraint model Q in PSDCone()
# The var_psd variable contains a reference to the constraint
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build_constraint(_error::Function,
Q::AbstractMatrix{<:AbstractJuMPScalar},
::PSDCone)

Return a VectorConstraint of shape SquareMatrixShape constraining the matrix Q to be symmetric and positive semidefinite.

This function is used by the @constraint and @SDconstraint macros as follows:

@constraint(model, Q in PSDCone())
@SDconstraint(model, P ⪰ Q)

The @constraint call above is usually used when the entries of Q are affine or quadratic expressions, but it can also be used when the entries are variables to get the reference of the semidefinite constraint, e.g.,

@variable model Q[1:2,1:2]
# The type of Q is Matrix{VariableRef}
var_psd = @constraint model Q in PSDCone()
# The var_psd variable contains a reference to the constraint
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##### Shapes

Shapes allow vector constraints, which are represented as flat vectors in MOI, to retain a matrix shape at the JuMP level. There is a shape field in VectorConstraint that can be set in build_constraint and that is used to reshape the result computed in value and dual.

JuMP.shapeFunction
shape(c::AbstractConstraint)::AbstractShape

Return the shape of the constraint c.

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JuMP.reshape_vectorFunction
reshape_vector(vectorized_form::Vector, shape::AbstractShape)

Return an object in its original shape shape given its vectorized form vectorized_form.

Examples

Given a SymmetricMatrixShape of vectorized form [1, 2, 3], the following code returns the matrix Symmetric(Matrix[1 2; 2 3]):

julia> reshape_vector([1, 2, 3], SymmetricMatrixShape(2))
2×2 LinearAlgebra.Symmetric{Int64,Array{Int64,2}}:
1  2
2  3
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JuMP.reshape_setFunction
reshape_set(vectorized_set::MOI.AbstractSet, shape::AbstractShape)

Return a set in its original shape shape given its vectorized form vectorized_form.

Examples

Given a SymmetricMatrixShape of vectorized form [1, 2, 3] in MOI.PositiveSemidefinieConeTriangle(2), the following code returns the set of the original constraint Symmetric(Matrix[1 2; 2 3]) in PSDCone():

julia> reshape_set(MOI.PositiveSemidefiniteConeTriangle(2), SymmetricMatrixShape(2))
PSDCone()
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JuMP.dual_shapeFunction
dual_shape(shape::AbstractShape)::AbstractShape

Returns the shape of the dual space of the space of objects of shape shape. By default, the dual_shape of a shape is itself. See the examples section below for an example for which this is not the case.

Examples

Consider polynomial constraints for which the dual is moment constraints and moment constraints for which the dual is polynomial constraints. Shapes for polynomials can be defined as follows:

struct Polynomial
coefficients::Vector{Float64}
monomials::Vector{Monomial}
end
struct PolynomialShape <: AbstractShape
monomials::Vector{Monomial}
end
JuMP.reshape_vector(x::Vector, shape::PolynomialShape) = Polynomial(x, shape.monomials)

and a shape for moments can be defined as follows:

struct Moments
coefficients::Vector{Float64}
monomials::Vector{Monomial}
end
struct MomentsShape <: AbstractShape
monomials::Vector{Monomial}
end
JuMP.reshape_vector(x::Vector, shape::MomentsShape) = Moments(x, shape.monomials)

Then dual_shape allows the definition of the shape of the dual of polynomial and moment constraints:

dual_shape(shape::PolynomialShape) = MomentsShape(shape.monomials)
dual_shape(shape::MomentsShape) = PolynomialShape(shape.monomials)
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JuMP.SquareMatrixShapeType
SquareMatrixShape

Shape object for a square matrix of side_dimension rows and columns. The vectorized form contains the entries of the the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

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JuMP.SymmetricMatrixShapeType
SymmetricMatrixShape

Shape object for a symmetric square matrix of side_dimension rows and columns. The vectorized form contains the entries of the upper-right triangular part of the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

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#### Adding add_constraint methods

JuMP.add_constraintFunction
add_constraint(model::Model, con::AbstractConstraint, name::String="")

Add a constraint con to Model model and sets its name.

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