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Add bridge from Hermitian PSD to complex function in Symmetric PSD (#2724)
* Add bridge from Hermitian PSD to complex function in Symmetric PSD * Fix docstring * Add to add_all_bridges * Fix format * Fix * Add tests * Add adjoint * Add test * Fix SetDotScaling * Add SingleBridgeOptimizer
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‎src/Bridges/Constraint/Constraint.jl

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@@ -56,6 +56,7 @@ function add_all_bridges(model, ::Type{T}) where {T}
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end
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MOI.Bridges.add_bridge(model, GreaterToLessBridge{T})
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MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
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MOI.Bridges.add_bridge(model, HermitianToComplexSymmetricBridge{T})
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MOI.Bridges.add_bridge(model, IndicatorActiveOnFalseBridge{T})
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MOI.Bridges.add_bridge(model, IndicatorGreaterToLessThanBridge{T})
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MOI.Bridges.add_bridge(model, IndicatorLessToGreaterThanBridge{T})

‎src/Bridges/Constraint/bridges/HermitianToComplexSymmetricBridge.jl

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# Copyright (c) 2017: Miles Lubin and contributors
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# Copyright (c) 2017: Google Inc.
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#
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# Use of this source code is governed by an MIT-style license that can be found
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# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
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"""
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HermitianToComplexSymmetricBridge{T,F,G} <: Bridges.Constraint.AbstractBridge
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`HermitianToSymmetricBridge` implements the following reformulation:
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* Hermitian positive semidefinite `n x n` represented as a vector of real
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entries with real and imaginary parts on different entries to a vector
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of complex entries.
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See also [`MOI.Bridges.Constraint.HermitianToSymmetricPSDBridge`](@ref).
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## Source node
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`HermitianToComplexSymmetricBridge` supports:
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* `G` in [`MOI.HermitianPositiveSemidefiniteConeTriangle`](@ref)
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## Target node
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`HermitianToComplexSymmetricBridge` creates:
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* `F` in [`MOI.PositiveSemidefiniteConeTriangle`](@ref)
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Note that if `G` is `MOI.VectorAffineFunction{T}` then `F` will be
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`MOI.VectorAffineFunction{Complex{T}}`
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"""
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struct HermitianToComplexSymmetricBridge{T,F,G} <: SetMapBridge{
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T,
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MOI.PositiveSemidefiniteConeTriangle,
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MOI.HermitianPositiveSemidefiniteConeTriangle,
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F,
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G,
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}
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constraint::MOI.ConstraintIndex{F,MOI.PositiveSemidefiniteConeTriangle}
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end
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const HermitianToComplexSymmetric{T,OT<:MOI.ModelLike} =
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SingleBridgeOptimizer{HermitianToComplexSymmetricBridge{T},OT}
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# Should be favored over `HermitianToSymmetricPSDBridge`
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MOI.Bridges.bridging_cost(::Type{<:HermitianToComplexSymmetricBridge}) = 0.5
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function _promote_complex_vcat(::Type{T}, ::Type{G}) where {T<:Real,G}
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S = MOI.Utilities.scalar_type(G)
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if S === T
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M = Complex{T}
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elseif S <: MOI.Utilities.TypedLike{T}
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M = MOI.Utilities.similar_type(S, Complex{T})
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else
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M = MOI.Utilities.promote_operation(*, Complex{T}, Complex{T}, S)
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end
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return MOI.Utilities.promote_operation(vcat, Complex{T}, M)
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end
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function concrete_bridge_type(
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::Type{<:HermitianToComplexSymmetricBridge{T}},
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G::Type{<:MOI.AbstractVectorFunction},
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::Type{MOI.HermitianPositiveSemidefiniteConeTriangle},
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) where {T}
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F = _promote_complex_vcat(T, G)
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return HermitianToComplexSymmetricBridge{T,F,G}
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end
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function MOI.Bridges.map_set(
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::Type{<:HermitianToComplexSymmetricBridge},
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set::MOI.HermitianPositiveSemidefiniteConeTriangle,
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)
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return MOI.PositiveSemidefiniteConeTriangle(set.side_dimension)
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end
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function MOI.Bridges.inverse_map_set(
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::Type{<:HermitianToComplexSymmetricBridge},
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set::MOI.PositiveSemidefiniteConeTriangle,
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)
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return MOI.HermitianPositiveSemidefiniteConeTriangle(set.side_dimension)
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end
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function MOI.Bridges.map_function(
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::Type{<:HermitianToComplexSymmetricBridge{T}},
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func,
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) where {T}
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complex_scalars = MOI.Utilities.eachscalar(func)
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S = MOI.Utilities.scalar_type(_promote_complex_vcat(T, typeof(func)))
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complex_dim = length(complex_scalars)
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complex_set = MOI.Utilities.set_with_dimension(
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MOI.HermitianPositiveSemidefiniteConeTriangle,
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complex_dim,
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)
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n = complex_set.side_dimension
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real_set = MOI.PositiveSemidefiniteConeTriangle(n)
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real_dim = MOI.dimension(real_set)
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real_scalars = Vector{S}(undef, real_dim)
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real_index = 0
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imag_index = real_dim
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for j in 1:n
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for i in 1:j
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real_index += 1
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if i == j
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real_scalars[real_index] = complex_scalars[real_index]
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else
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imag_index += 1
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real_scalars[real_index] =
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one(Complex{T}) * complex_scalars[real_index] +
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(one(T) * im) * complex_scalars[imag_index]
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end
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end
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end
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@assert length(real_scalars) == real_index
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@assert length(complex_scalars) == imag_index
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return MOI.Utilities.vectorize(real_scalars)
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end
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function MOI.Bridges.inverse_adjoint_map_function(
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BT::Type{<:HermitianToComplexSymmetricBridge},
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func,
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)
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return MOI.Bridges.map_function(BT, func)
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end
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function MOI.Bridges.inverse_map_function(
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::Type{<:HermitianToComplexSymmetricBridge},
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func,
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)
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real_scalars = MOI.Utilities.eachscalar(func)
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real_set = MOI.Utilities.set_with_dimension(
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MOI.PositiveSemidefiniteConeTriangle,
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length(real_scalars),
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)
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n = real_set.side_dimension
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complex_set = MOI.HermitianPositiveSemidefiniteConeTriangle(n)
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complex_scalars = Vector{
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MA.promote_operation(real, MOI.Utilities.scalar_type(typeof(func))),
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}(
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undef,
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MOI.dimension(complex_set),
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)
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real_index = 0
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imag_index = MOI.dimension(real_set)
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for j in 1:n
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for i in 1:j
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real_index += 1
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complex_scalars[real_index] = real(real_scalars[real_index])
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if i != j
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imag_index += 1
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complex_scalars[imag_index] = imag(real_scalars[real_index])
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end
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end
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end
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@assert length(real_scalars) == real_index
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@assert length(complex_scalars) == imag_index
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return MOI.Utilities.vectorize(complex_scalars)
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end
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function MOI.Bridges.adjoint_map_function(
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BT::Type{<:HermitianToComplexSymmetricBridge},
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func,
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)
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return MOI.Bridges.inverse_map_function(BT, func)
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end

‎src/Bridges/Constraint/bridges/HermitianToSymmetricPSDBridge.jl

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@@ -153,7 +153,7 @@ function MOI.Bridges.map_function(
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end
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function MOI.Bridges.inverse_map_function(
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BT::Type{<:HermitianToSymmetricPSDBridge},
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::Type{<:HermitianToSymmetricPSDBridge},
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func,
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)
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real_scalars = MOI.Utilities.eachscalar(func)

‎src/Bridges/Constraint/bridges/SetDotScalingBridge.jl

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# for `SetMapBridge` does not work
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function MOI.supports_constraint(
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::Type{<:SetDotScalingBridge},
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::Type{<:MOI.AbstractVectorFunction},
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F::Type{<:MOI.AbstractVectorFunction},
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S::Type{<:MOI.AbstractVectorSet},
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)
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return MOI.is_set_dot_scaled(S)
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return !MOI.Utilities.is_complex(F) && MOI.is_set_dot_scaled(S)
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end
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function MOI.supports_constraint(

‎test/Bridges/Constraint/HermitianToComplexSymmetricBridge.jl

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# Copyright (c) 2017: Miles Lubin and contributors
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# Copyright (c) 2017: Google Inc.
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#
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# Use of this source code is governed by an MIT-style license that can be found
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# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
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module TestConstraintHermitianToComplexSymmetric
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using Test
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import MathOptInterface as MOI
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function runtests()
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for name in names(@__MODULE__; all = true)
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if startswith("$(name)", "test_")
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@testset "$(name)" begin
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getfield(@__MODULE__, name)()
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end
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end
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end
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return
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end
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function test_dimension_2()
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MOI.Bridges.runtests(
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MOI.Bridges.Constraint.HermitianToComplexSymmetricBridge,
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model -> begin
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a, b, c = MOI.add_variables(model, 3)
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MOI.add_constraint(
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model,
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MOI.Utilities.vectorize([
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1.0 * a + 2.0 * b,
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3.0 * c,
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4.0 * b,
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5.0 * a,
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]),
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MOI.HermitianPositiveSemidefiniteConeTriangle(2),
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)
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end,
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model -> begin
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a, b, c = MOI.add_variables(model, 3)
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MOI.add_constraint(
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model,
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MOI.Utilities.vectorize([
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Complex(1.0) * a + Complex(2.0) * b,
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Complex(3.0) * c + 5.0 * im * a,
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Complex(4.0) * b,
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]),
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MOI.PositiveSemidefiniteConeTriangle(2),
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)
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end,
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)
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return
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end
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function test_dimension_3()
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MOI.Bridges.runtests(
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MOI.Bridges.Constraint.HermitianToComplexSymmetricBridge,
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model -> begin
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x = MOI.add_variables(model, 9)
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MOI.add_constraint(
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model,
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MOI.VectorOfVariables(x),
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MOI.HermitianPositiveSemidefiniteConeTriangle(3),
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)
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end,
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model -> begin
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x = MOI.add_variables(model, 9)
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MOI.add_constraint(
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model,
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MOI.Utilities.vectorize([
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Complex(1.0) * x[1],
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Complex(1.0) * x[2] + 1.0 * im * x[7],
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Complex(1.0) * x[3],
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Complex(1.0) * x[4] + 1.0 * im * x[8],
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Complex(1.0) * x[5] + 1.0 * im * x[9],
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Complex(1.0) * x[6],
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]),
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MOI.PositiveSemidefiniteConeTriangle(3),
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)
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end,
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)
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return
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end
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end # module
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TestConstraintHermitianToComplexSymmetric.runtests()

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