diff --git a/src/Bridges/Constraint/Constraint.jl b/src/Bridges/Constraint/Constraint.jl
index 65af0f4d02..d9d3c84074 100644
--- a/src/Bridges/Constraint/Constraint.jl
+++ b/src/Bridges/Constraint/Constraint.jl
@@ -36,6 +36,7 @@ include("bridges/geomean.jl")
 include("bridges/indicator_activate_on_zero.jl")
 include("bridges/indicator_flipsign.jl")
 include("bridges/indicator_sos.jl")
+include("bridges/inequality_to_complements.jl")
 include("bridges/integer_to_zeroone.jl")
 include("bridges/interval.jl")
 include("bridges/ltgt_to_interval.jl")
@@ -135,6 +136,7 @@ function add_all_bridges(bridged_model, ::Type{T}) where {T}
     MOI.Bridges.add_bridge(bridged_model, SemiToBinaryBridge{T})
     MOI.Bridges.add_bridge(bridged_model, ZeroOneBridge{T})
     MOI.Bridges.add_bridge(bridged_model, IntegerToZeroOneBridge{T})
+    MOI.Bridges.add_bridge(bridged_model, InequalityToComplementsBridge{T})
     # Do not add by default
     # MOI.Bridges.add_bridge(bridged_model, NumberConversionBridge{T})
     # Constraint programming bridges
diff --git a/src/Bridges/Constraint/bridges/inequality_to_complements.jl b/src/Bridges/Constraint/bridges/inequality_to_complements.jl
new file mode 100644
index 0000000000..c0850f3bcb
--- /dev/null
+++ b/src/Bridges/Constraint/bridges/inequality_to_complements.jl
@@ -0,0 +1,151 @@
+# Copyright (c) 2017: Miles Lubin and contributors
+# Copyright (c) 2017: Google Inc.
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+"""
+    InequalityToComplementsBridge{T,F,S,G} <: Bridges.Constraint.AbstractBridge
+
+`InequalityToComplementsBridge` implements the following reformulations:
+
+  * ``f(x) \\ge b`` into ``\\exists y`` such that ``f(x) - b \\perp y \\ge 0``
+  * ``f(x) \\le b`` into ``f(x) - b \\perp y \\le 0``
+  * ``f(x) = b`` into ``f(x) - b \\perp y``
+
+## Source node
+
+`InequalityToComplementsBridge` supports:
+
+  * `F` in [`MOI.GreaterThan{T}`](@ref)
+  * `F` in [`MOI.LessThan{T}`](@ref)
+  * `F` in [`MOI.EqualTo`](@ref)
+
+## Target nodes
+
+`InequalityToComplementsBridge` creates:
+
+  * [`MOI.VariableIndex`](@ref) in [`MOI.LessThan{T}`](@ref)
+  * [`MOI.VariableIndex`](@ref) in [`MOI.GreaterThan{T}`](@ref)
+  * `G` in [`MOI.Complements`](@ref)
+"""
+mutable struct InequalityToComplementsBridge{
+    T,
+    F<:MOI.AbstractScalarFunction,
+    S<:Union{MOI.GreaterThan{T},MOI.LessThan{T},MOI.EqualTo{T}},
+    G<:MOI.AbstractVectorFunction,
+} <: AbstractBridge
+    y::MOI.VariableIndex
+    set::S
+    ci::MOI.ConstraintIndex{G,MOI.Complements}
+end
+
+const InequalityToComplements{T,OT<:MOI.ModelLike} =
+    SingleBridgeOptimizer{InequalityToComplementsBridge{T},OT}
+
+function _add_y_variable(model, ::MOI.GreaterThan{T}) where {T}
+    return MOI.add_constrained_variable(model, MOI.GreaterThan(zero(T)))[1]
+end
+
+function _add_y_variable(model, ::MOI.LessThan{T}) where {T}
+    return MOI.add_constrained_variable(model, MOI.LessThan(zero(T)))[1]
+end
+
+_add_y_variable(model, ::MOI.EqualTo) = MOI.add_variable(model)
+
+function bridge_constraint(
+    ::Type{InequalityToComplementsBridge{T,F,S,G}},
+    model::MOI.ModelLike,
+    f::F,
+    set::S,
+) where {T,F,S<:Union{MOI.GreaterThan{T},MOI.LessThan{T},MOI.EqualTo{T}},G}
+    y = _add_y_variable(model, set)
+    f_set = MOI.Utilities.operate(-, T, f, MOI.constant(set))
+    g = MOI.Utilities.operate(vcat, T, f_set, y)
+    ci = MOI.add_constraint(model, g, MOI.Complements(2))
+    return InequalityToComplementsBridge{T,F,S,G}(y, set, ci)
+end
+
+function MOI.supports_constraint(
+    ::Type{<:InequalityToComplementsBridge{T}},
+    ::Type{F},
+    ::Type{<:Union{MOI.GreaterThan{T},MOI.LessThan{T},MOI.EqualTo{T}}},
+) where {T,F<:MOI.AbstractScalarFunction}
+    return !MOI.Utilities.is_complex(F)
+end
+
+function MOI.Bridges.added_constrained_variable_types(
+    ::Type{InequalityToComplementsBridge{T,F,S,G}},
+) where {T,F,S<:Union{MOI.GreaterThan{T},MOI.LessThan{T}},G}
+    return Tuple{Type}[(S,)]
+end
+
+function MOI.Bridges.added_constrained_variable_types(
+    ::Type{InequalityToComplementsBridge{T,F,MOI.EqualTo{T},G}},
+) where {T,F,G}
+    return Tuple{Type}[(MOI.Reals,)]
+end
+
+function MOI.Bridges.added_constraint_types(
+    ::Type{InequalityToComplementsBridge{T,F,S,G}},
+) where {T,F,S,G}
+    return Tuple{Type,Type}[(G, MOI.Complements)]
+end
+
+function concrete_bridge_type(
+    ::Type{<:InequalityToComplementsBridge},
+    F::Type{<:MOI.AbstractScalarFunction},
+    S::Type{<:Union{MOI.GreaterThan{T},MOI.LessThan{T},MOI.EqualTo{T}}},
+) where {T}
+    G = MOI.Utilities.promote_operation(vcat, T, F, MOI.VariableIndex)
+    return InequalityToComplementsBridge{T,F,S,G}
+end
+
+function MOI.get(::InequalityToComplementsBridge, ::MOI.NumberOfVariables)
+    return Int64(1)
+end
+
+function MOI.get(
+    bridge::InequalityToComplementsBridge,
+    ::MOI.ListOfVariableIndices,
+)
+    return [bridge.y]
+end
+
+function MOI.get(
+    ::InequalityToComplementsBridge{T,F,S,G},
+    ::MOI.NumberOfConstraints{G,MOI.Complements},
+)::Int64 where {T,F,S,G}
+    return 1
+end
+
+function MOI.get(
+    bridge::InequalityToComplementsBridge{T,F,S,G},
+    ::MOI.ListOfConstraintIndices{G,MOI.Complements},
+) where {T,F,S,G}
+    return [bridge.ci]
+end
+
+function MOI.delete(model::MOI.ModelLike, bridge::InequalityToComplementsBridge)
+    MOI.delete(model, bridge.y)
+    MOI.delete(model, bridge.ci)
+    return
+end
+
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::MOI.ConstraintFunction,
+    bridge::InequalityToComplementsBridge{T},
+) where {T}
+    g = MOI.get(model, attr, bridge.ci)
+    f_set = first(MOI.Utilities.scalarize(g))
+    return MOI.Utilities.operate(+, T, f_set, MOI.constant(bridge.set))
+end
+
+function MOI.get(
+    ::MOI.ModelLike,
+    ::MOI.ConstraintSet,
+    bridge::InequalityToComplementsBridge,
+)
+    return bridge.set
+end
diff --git a/test/Bridges/Constraint/inequality_to_complements.jl b/test/Bridges/Constraint/inequality_to_complements.jl
new file mode 100644
index 0000000000..975816be29
--- /dev/null
+++ b/test/Bridges/Constraint/inequality_to_complements.jl
@@ -0,0 +1,173 @@
+# Copyright (c) 2017: Miles Lubin and contributors
+# Copyright (c) 2017: Google Inc.
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+module TestConstraintInequalityToComplements
+
+using Test
+
+import MathOptInterface as MOI
+
+function runtests()
+    for name in names(@__MODULE__; all = true)
+        if startswith("$(name)", "test_")
+            @testset "$(name)" begin
+                getfield(@__MODULE__, name)()
+            end
+        end
+    end
+    return
+end
+
+function test_runtests_GreaterThan()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        1.0 * x >= 0.0
+        """,
+        """
+        variables: x, y
+        [1.0 * x, y] in Complements(2)
+        y >= 0.0
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x >= 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x + -3.0, y] in Complements(2)
+        y >= 0.0
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x * x >= 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x * x + -3.0, y] in Complements(2)
+        y >= 0.0
+        """,
+    )
+    return
+end
+
+function test_runtests_LessThan()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        1.0 * x <= 0.0
+        """,
+        """
+        variables: x, y
+        [1.0 * x, y] in Complements(2)
+        y <= 0.0
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x <= 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x + -3.0, y] in Complements(2)
+        y <= 0.0
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x * x <= 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x * x + -3.0, y] in Complements(2)
+        y <= 0.0
+        """,
+    )
+    return
+end
+
+function test_runtests_EqualTo()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        1.0 * x == 0.0
+        """,
+        """
+        variables: x, y
+        [1.0 * x, y] in Complements(2)
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x == 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x + -3.0, y] in Complements(2)
+        """,
+    )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.InequalityToComplementsBridge,
+        """
+        variables: x
+        2.0 * x * x == 3.0
+        """,
+        """
+        variables: x, y
+        [2.0 * x * x + -3.0, y] in Complements(2)
+        """,
+    )
+    return
+end
+
+function test_ScalarNonlinearFunction()
+    # We can't use the standard runtests because ScalarNonlinearFunction does
+    # not preserve f(x) ≈ (f(x) - g(x)) + g(x)
+    for set in (MOI.EqualTo(1.0), MOI.LessThan(1.0), MOI.GreaterThan(1.0))
+        inner = MOI.Utilities.Model{Float64}()
+        model = MOI.Bridges.Constraint.InequalityToComplements{Float64}(inner)
+        x = MOI.add_variable(model)
+        f = MOI.ScalarNonlinearFunction(:sin, Any[x])
+        c = MOI.add_constraint(model, f, set)
+        F, S = MOI.VectorNonlinearFunction, MOI.Complements
+        indices = MOI.get(inner, MOI.ListOfConstraintIndices{F,S}())
+        @test length(indices) == 1
+        inner_variables = MOI.get(inner, MOI.ListOfVariableIndices())
+        @test length(inner_variables) == 2
+        u, v = inner_variables
+        u_sin = MOI.ScalarNonlinearFunction(:sin, Any[u])
+        g = MOI.VectorNonlinearFunction([
+            MOI.ScalarNonlinearFunction(:-, Any[u_sin, 1.0]),
+            MOI.ScalarNonlinearFunction(:+, Any[v]),
+        ])
+        @test ≈(MOI.get(inner, MOI.ConstraintFunction(), indices[1]), g)
+        h = MOI.ScalarNonlinearFunction(
+            :+,
+            Any[MOI.ScalarNonlinearFunction(:-, Any[f, 1.0]), 1.0],
+        )
+        @test ≈(MOI.get(model, MOI.ConstraintFunction(), c), h)
+    end
+    return
+end
+
+end  # module
+
+TestConstraintInequalityToComplements.runtests()