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Merged
blegat merged 2 commits into from
Dec 4, 2025
Merged

Add support for nonlinear expressions in MOI.Complements #8

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2ea267e
add support for nonlinear expressions in MOI.Complements
frapac Oct 30, 2025
3a163d8
operate!
blegat Dec 4, 2025
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29 changes: 8 additions & 21 deletions src/vertical.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,7 @@
const VF = Union{
MOI.VectorAffineFunction,
MOI.VectorQuadraticFunction,
MOI.VectorNonlinearFunction,
}

function has_complementarity(model::MOI.ModelLike)
Expand Down Expand Up @@ -29,28 +30,13 @@ function _is_single_variable(func::MOI.ScalarQuadraticFunction)
false
end
end
function _is_single_variable(func::MOI.ScalarNonlinearFunction)
return func.head == :+ && length(func.args) == 1 && isa(func.args[1], MOI.VariableIndex)
end
_get_variable(func::MOI.ScalarAffineFunction) = func.terms[1].variable
_get_variable(func::MOI.ScalarQuadraticFunction) = func.affine_terms[1].variable
_get_variable(func::MOI.ScalarNonlinearFunction) = func.args[1]

# Reformulate
function _vertical_formulation!(model, terms::Vector{MOI.ScalarAffineTerm{T}}, c::T) where T
x = MOI.add_variable(model)
push!(terms, MOI.ScalarAffineTerm{T}(-one(T), x))
func = MOI.ScalarAffineFunction{T}(terms, zero(T))
MOI.add_constraint(model, func, MOI.EqualTo{T}(-c))
return x
end

function _add_slack!(model, func::MOI.ScalarAffineFunction{T}) where T
x = MOI.add_variable(model)
push!(func.terms, MOI.ScalarAffineTerm{T}(-one(T), x))
return x
end
function _add_slack!(model, func::MOI.ScalarQuadraticFunction{T}) where T
x = MOI.add_variable(model)
push!(func.affine_terms, MOI.ScalarAffineTerm{T}(-one(T), x))
return x
end

# TODO: add support for ScalarNonlinearTerm
function _parse_complementarity_constraint(fun::MOI.AbstractVectorFunction, n_comp)
Expand Down Expand Up @@ -129,8 +115,9 @@ function reformulate_to_vertical!(model::MOI.ModelLike)
push!(ind_cc2, x2)
else
# Else, reformulate LHS using vertical form
x1 = _add_slack!(model, lhs)
MOI.add_constraint(model, lhs, MOI.EqualTo{Float64}(0))
x1 = MOI.add_variable(model)
new_lhs = MOIU.operate(-, Float64, lhs, x1)
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MOI.add_constraint(model, new_lhs, MOI.EqualTo{Float64}(0))
push!(ind_cc1, x1)
push!(ind_cc2, x2)
end
Expand Down
43 changes: 42 additions & 1 deletion test/runtests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -21,13 +21,34 @@ function fletcher_leyffer_ex1_nonlinear_model()
return model
end

function nonlinear_test_model()
model = Model()
@variable(model, x >= 0.0)
@variable(model, y >= 0.0)
@objective(model, Min, x^2 + y^2 - 4*x*y)
# Build complementarity constraints with nonlinear expression
@constraint(model, [sin(x), y] ∈ MOI.Complements(2))
return model
end

function nonlinear_test_reformulated_model()
model = Model()
@variable(model, x >= 0.0)
@variable(model, y >= 0.0)
@variable(model, slack)
@objective(model, Min, x^2 + y^2 - 4*x*y)
# Build complementarity constraints with nonlinear expression
@constraint(model, sin(x) == slack)
@constraint(model, slack * y <= 0.0)
return model
end

expected_models = Dict(
Instances.fletcher_leyffer_ex1_model => fletcher_leyffer_ex1_nonlinear_model,
)

function test_model(model_func)
model = model_func()
model = Instances.fletcher_leyffer_ex1_model()
inner = MOI.Utilities.Model{Float64}()
set_optimizer(model, () -> ComplementOpt.Optimizer(inner))
MOI.Utilities.attach_optimizer(model)
Expand All @@ -42,6 +63,20 @@ function test_model(model_func)
end
end

function test_nonlinear_expr()
model = nonlinear_test_model()
inner = MOI.Utilities.Model{Float64}()
set_optimizer(model, () -> ComplementOpt.Optimizer(inner))
MOI.Utilities.attach_optimizer(model)
MOI.Utilities.attach_optimizer(backend(model).optimizer.model)

expected = nonlinear_test_reformulated_model()
MOI.Bridges._test_structural_identical(
unsafe_backend(model).optimizer,
backend(expected),
)
end

instances = filter(names(Instances; all = true)) do name
# The function types start with `#`
s = String(name)
Expand All @@ -51,3 +86,9 @@ end
@testset "$name" for name in instances
test_model(getfield(Instances, name))
end

@testset "Unit-tests" begin
test_nonlinear_expr()
end


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