diff --git a/src/Bridges/Constraint/Constraint.jl b/src/Bridges/Constraint/Constraint.jl
index 859e0ef766..197e1e5bfe 100644
--- a/src/Bridges/Constraint/Constraint.jl
+++ b/src/Bridges/Constraint/Constraint.jl
@@ -56,6 +56,7 @@ function add_all_bridges(model, ::Type{T}) where {T}
     end
     MOI.Bridges.add_bridge(model, GreaterToLessBridge{T})
     MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
+    MOI.Bridges.add_bridge(model, HermitianToComplexSymmetricBridge{T})
     MOI.Bridges.add_bridge(model, IndicatorActiveOnFalseBridge{T})
     MOI.Bridges.add_bridge(model, IndicatorGreaterToLessThanBridge{T})
     MOI.Bridges.add_bridge(model, IndicatorLessToGreaterThanBridge{T})
diff --git a/src/Bridges/Constraint/bridges/HermitianToComplexSymmetricBridge.jl b/src/Bridges/Constraint/bridges/HermitianToComplexSymmetricBridge.jl
new file mode 100644
index 0000000000..ff5a02f94e
--- /dev/null
+++ b/src/Bridges/Constraint/bridges/HermitianToComplexSymmetricBridge.jl
@@ -0,0 +1,165 @@
+# 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.
+
+"""
+    HermitianToComplexSymmetricBridge{T,F,G} <: Bridges.Constraint.AbstractBridge
+
+`HermitianToSymmetricBridge` implements the following reformulation:
+
+  * Hermitian positive semidefinite `n x n` represented as a vector of real
+    entries with real and imaginary parts on different entries to a vector
+    of complex entries.
+
+See also [`MOI.Bridges.Constraint.HermitianToSymmetricPSDBridge`](@ref).
+
+## Source node
+
+`HermitianToComplexSymmetricBridge` supports:
+
+  * `G` in [`MOI.HermitianPositiveSemidefiniteConeTriangle`](@ref)
+
+## Target node
+
+`HermitianToComplexSymmetricBridge` creates:
+
+  * `F` in [`MOI.PositiveSemidefiniteConeTriangle`](@ref)
+
+Note that if `G` is `MOI.VectorAffineFunction{T}` then `F` will be
+`MOI.VectorAffineFunction{Complex{T}}`
+"""
+struct HermitianToComplexSymmetricBridge{T,F,G} <: SetMapBridge{
+    T,
+    MOI.PositiveSemidefiniteConeTriangle,
+    MOI.HermitianPositiveSemidefiniteConeTriangle,
+    F,
+    G,
+}
+    constraint::MOI.ConstraintIndex{F,MOI.PositiveSemidefiniteConeTriangle}
+end
+
+const HermitianToComplexSymmetric{T,OT<:MOI.ModelLike} =
+    SingleBridgeOptimizer{HermitianToComplexSymmetricBridge{T},OT}
+
+# Should be favored over `HermitianToSymmetricPSDBridge`
+MOI.Bridges.bridging_cost(::Type{<:HermitianToComplexSymmetricBridge}) = 0.5
+
+function _promote_complex_vcat(::Type{T}, ::Type{G}) where {T<:Real,G}
+    S = MOI.Utilities.scalar_type(G)
+    if S === T
+        M = Complex{T}
+    elseif S <: MOI.Utilities.TypedLike{T}
+        M = MOI.Utilities.similar_type(S, Complex{T})
+    else
+        M = MOI.Utilities.promote_operation(*, Complex{T}, Complex{T}, S)
+    end
+    return MOI.Utilities.promote_operation(vcat, Complex{T}, M)
+end
+
+function concrete_bridge_type(
+    ::Type{<:HermitianToComplexSymmetricBridge{T}},
+    G::Type{<:MOI.AbstractVectorFunction},
+    ::Type{MOI.HermitianPositiveSemidefiniteConeTriangle},
+) where {T}
+    F = _promote_complex_vcat(T, G)
+    return HermitianToComplexSymmetricBridge{T,F,G}
+end
+
+function MOI.Bridges.map_set(
+    ::Type{<:HermitianToComplexSymmetricBridge},
+    set::MOI.HermitianPositiveSemidefiniteConeTriangle,
+)
+    return MOI.PositiveSemidefiniteConeTriangle(set.side_dimension)
+end
+
+function MOI.Bridges.inverse_map_set(
+    ::Type{<:HermitianToComplexSymmetricBridge},
+    set::MOI.PositiveSemidefiniteConeTriangle,
+)
+    return MOI.HermitianPositiveSemidefiniteConeTriangle(set.side_dimension)
+end
+
+function MOI.Bridges.map_function(
+    ::Type{<:HermitianToComplexSymmetricBridge{T}},
+    func,
+) where {T}
+    complex_scalars = MOI.Utilities.eachscalar(func)
+    S = MOI.Utilities.scalar_type(_promote_complex_vcat(T, typeof(func)))
+    complex_dim = length(complex_scalars)
+    complex_set = MOI.Utilities.set_with_dimension(
+        MOI.HermitianPositiveSemidefiniteConeTriangle,
+        complex_dim,
+    )
+    n = complex_set.side_dimension
+    real_set = MOI.PositiveSemidefiniteConeTriangle(n)
+    real_dim = MOI.dimension(real_set)
+    real_scalars = Vector{S}(undef, real_dim)
+    real_index = 0
+    imag_index = real_dim
+    for j in 1:n
+        for i in 1:j
+            real_index += 1
+            if i == j
+                real_scalars[real_index] = complex_scalars[real_index]
+            else
+                imag_index += 1
+                real_scalars[real_index] =
+                    one(Complex{T}) * complex_scalars[real_index] +
+                    (one(T) * im) * complex_scalars[imag_index]
+            end
+        end
+    end
+    @assert length(real_scalars) == real_index
+    @assert length(complex_scalars) == imag_index
+    return MOI.Utilities.vectorize(real_scalars)
+end
+
+function MOI.Bridges.inverse_adjoint_map_function(
+    BT::Type{<:HermitianToComplexSymmetricBridge},
+    func,
+)
+    return MOI.Bridges.map_function(BT, func)
+end
+
+function MOI.Bridges.inverse_map_function(
+    ::Type{<:HermitianToComplexSymmetricBridge},
+    func,
+)
+    real_scalars = MOI.Utilities.eachscalar(func)
+    real_set = MOI.Utilities.set_with_dimension(
+        MOI.PositiveSemidefiniteConeTriangle,
+        length(real_scalars),
+    )
+    n = real_set.side_dimension
+    complex_set = MOI.HermitianPositiveSemidefiniteConeTriangle(n)
+    complex_scalars = Vector{
+        MA.promote_operation(real, MOI.Utilities.scalar_type(typeof(func))),
+    }(
+        undef,
+        MOI.dimension(complex_set),
+    )
+    real_index = 0
+    imag_index = MOI.dimension(real_set)
+    for j in 1:n
+        for i in 1:j
+            real_index += 1
+            complex_scalars[real_index] = real(real_scalars[real_index])
+            if i != j
+                imag_index += 1
+                complex_scalars[imag_index] = imag(real_scalars[real_index])
+            end
+        end
+    end
+    @assert length(real_scalars) == real_index
+    @assert length(complex_scalars) == imag_index
+    return MOI.Utilities.vectorize(complex_scalars)
+end
+
+function MOI.Bridges.adjoint_map_function(
+    BT::Type{<:HermitianToComplexSymmetricBridge},
+    func,
+)
+    return MOI.Bridges.inverse_map_function(BT, func)
+end
diff --git a/src/Bridges/Constraint/bridges/HermitianToSymmetricPSDBridge.jl b/src/Bridges/Constraint/bridges/HermitianToSymmetricPSDBridge.jl
index 0283e29845..81ad558682 100644
--- a/src/Bridges/Constraint/bridges/HermitianToSymmetricPSDBridge.jl
+++ b/src/Bridges/Constraint/bridges/HermitianToSymmetricPSDBridge.jl
@@ -153,7 +153,7 @@ function MOI.Bridges.map_function(
 end
 
 function MOI.Bridges.inverse_map_function(
-    BT::Type{<:HermitianToSymmetricPSDBridge},
+    ::Type{<:HermitianToSymmetricPSDBridge},
     func,
 )
     real_scalars = MOI.Utilities.eachscalar(func)
diff --git a/src/Bridges/Constraint/bridges/SetDotScalingBridge.jl b/src/Bridges/Constraint/bridges/SetDotScalingBridge.jl
index 9fff52e8ba..e778d4019b 100644
--- a/src/Bridges/Constraint/bridges/SetDotScalingBridge.jl
+++ b/src/Bridges/Constraint/bridges/SetDotScalingBridge.jl
@@ -194,10 +194,10 @@ end
 # for `SetMapBridge` does not work
 function MOI.supports_constraint(
     ::Type{<:SetDotScalingBridge},
-    ::Type{<:MOI.AbstractVectorFunction},
+    F::Type{<:MOI.AbstractVectorFunction},
     S::Type{<:MOI.AbstractVectorSet},
 )
-    return MOI.is_set_dot_scaled(S)
+    return !MOI.Utilities.is_complex(F) && MOI.is_set_dot_scaled(S)
 end
 
 function MOI.supports_constraint(
diff --git a/test/Bridges/Constraint/HermitianToComplexSymmetricBridge.jl b/test/Bridges/Constraint/HermitianToComplexSymmetricBridge.jl
new file mode 100644
index 0000000000..0a02e1574a
--- /dev/null
+++ b/test/Bridges/Constraint/HermitianToComplexSymmetricBridge.jl
@@ -0,0 +1,88 @@
+# 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 TestConstraintHermitianToComplexSymmetric
+
+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_dimension_2()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.HermitianToComplexSymmetricBridge,
+        model -> begin
+            a, b, c = MOI.add_variables(model, 3)
+            MOI.add_constraint(
+                model,
+                MOI.Utilities.vectorize([
+                    1.0 * a + 2.0 * b,
+                    3.0 * c,
+                    4.0 * b,
+                    5.0 * a,
+                ]),
+                MOI.HermitianPositiveSemidefiniteConeTriangle(2),
+            )
+        end,
+        model -> begin
+            a, b, c = MOI.add_variables(model, 3)
+            MOI.add_constraint(
+                model,
+                MOI.Utilities.vectorize([
+                    Complex(1.0) * a + Complex(2.0) * b,
+                    Complex(3.0) * c + 5.0 * im * a,
+                    Complex(4.0) * b,
+                ]),
+                MOI.PositiveSemidefiniteConeTriangle(2),
+            )
+        end,
+    )
+    return
+end
+
+function test_dimension_3()
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.HermitianToComplexSymmetricBridge,
+        model -> begin
+            x = MOI.add_variables(model, 9)
+            MOI.add_constraint(
+                model,
+                MOI.VectorOfVariables(x),
+                MOI.HermitianPositiveSemidefiniteConeTriangle(3),
+            )
+        end,
+        model -> begin
+            x = MOI.add_variables(model, 9)
+            MOI.add_constraint(
+                model,
+                MOI.Utilities.vectorize([
+                    Complex(1.0) * x[1],
+                    Complex(1.0) * x[2] + 1.0 * im * x[7],
+                    Complex(1.0) * x[3],
+                    Complex(1.0) * x[4] + 1.0 * im * x[8],
+                    Complex(1.0) * x[5] + 1.0 * im * x[9],
+                    Complex(1.0) * x[6],
+                ]),
+                MOI.PositiveSemidefiniteConeTriangle(3),
+            )
+        end,
+    )
+    return
+end
+
+end  # module
+
+TestConstraintHermitianToComplexSymmetric.runtests()