Dual sets

docs/src/apireference.md

@@ -288,6 +288,7 @@ AbstractVectorSet
 Functions for getting properties of sets.
 ```@docs
 dimension
+dual_set
 constant(s::EqualTo)
 supports_dimension_update
 update_dimension

src/sets.jl

@@ -30,6 +30,31 @@ julia> dimension(PositiveSemidefiniteConeTriangle(2))
 """
 function dimension end
 
+"""
+    dual_set(s::AbstractSet)
+
+Return the dual set of `s`, that is the dual cone of the set. This follows the 
+definition of duality discussed in [Duals](@ref).
+See [Dual cone](https://en.wikipedia.org/wiki/Dual_cone_and_polar_cone) for more information.
+If the dual cone is not defined it returns an error.
+
+### Examples
+
+```jldocstest
+julia> dual_set(Reals(4))
+Zeros(4)
+
+julia> dual_set(SecondOrderCone(5))
+SecondOrderCone(5)
+
+julia> dual_set(ExponentialCone())
+DualExponentialCone()
+```
+"""
+function dual_set end
+
+dual_set(s::AbstractSet) = error("Dual of $s is not implemented.")
+
 """
     AbstractScalarSet
 
@@ -59,6 +84,8 @@ struct Reals <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::Reals) = Zeros(dimension(s))
+
 """
     Zeros(dimension)
 
@@ -68,6 +95,8 @@ struct Zeros <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::Zeros) = Reals(dimension(s))
+
 """
     Nonnegatives(dimension)
 
@@ -77,6 +106,8 @@ struct Nonnegatives <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::Nonnegatives) = copy(s)
+
 """
     Nonpositives(dimension)
 
@@ -86,6 +117,8 @@ struct Nonpositives <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::Nonpositives) = copy(s)
+
 """
     GreaterThan{T <: Real}(lower::T)
 
@@ -158,6 +191,8 @@ struct SecondOrderCone <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::SecondOrderCone) = copy(s)
+
 """
     RotatedSecondOrderCone(dimension)
 
@@ -167,6 +202,8 @@ struct RotatedSecondOrderCone <: AbstractVectorSet
     dimension::Int
 end
 
+dual_set(s::RotatedSecondOrderCone) = copy(s)
+
 """
     GeometricMeanCone(dimension)
 
@@ -183,13 +220,17 @@ The 3-dimensional exponential cone ``\\{ (x,y,z) \\in \\mathbb{R}^3 : y \\exp (x
 """
 struct ExponentialCone <: AbstractVectorSet end
 
+dual_set(s::ExponentialCone) = DualExponentialCone()
+
 """
     DualExponentialCone()
 
 The 3-dimensional dual exponential cone ``\\{ (u,v,w) \\in \\mathbb{R}^3 : -u \\exp (v/u) \\le \\exp(1) w, u < 0 \\}``.
 """
 struct DualExponentialCone <: AbstractVectorSet end
 
+dual_set(s::DualExponentialCone) = ExponentialCone()
+
 """
     PowerCone{T <: Real}(exponent::T)
 
@@ -199,6 +240,8 @@ struct PowerCone{T <: Real} <: AbstractVectorSet
     exponent::T
 end
 
+dual_set(s::PowerCone{T}) where T <: Real = DualPowerCone{T}(s.exponent)
+
 """
     DualPowerCone{T <: Real}(exponent::T)
 
@@ -208,6 +251,8 @@ struct DualPowerCone{T <: Real} <: AbstractVectorSet
     exponent::T
 end
 
+dual_set(s::DualPowerCone{T}) where T <: Real = PowerCone{T}(s.exponent)
+
 dimension(s::Union{ExponentialCone, DualExponentialCone, PowerCone, DualPowerCone}) = 3
 
 """
@@ -383,6 +428,8 @@ struct PositiveSemidefiniteConeTriangle <: AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
 end
 
+dual_set(s::PositiveSemidefiniteConeTriangle) = copy(s)
+
 """
     PositiveSemidefiniteConeSquare(side_dimension) <: AbstractSymmetricMatrixSetSquare
 
@@ -411,6 +458,11 @@ struct PositiveSemidefiniteConeSquare <: AbstractSymmetricMatrixSetSquare
     side_dimension::Int
 end
 
+function dual_set(s::PositiveSemidefiniteConeSquare)
+    return error("""Dual of $s is not defined in MathOptInterface.
+                    For more details see the comments in src/Bridges/Constraint/square.jl""")
+end
+
 triangular_form(::Type{PositiveSemidefiniteConeSquare}) = PositiveSemidefiniteConeTriangle
 
 """

test/Utilities/sets.jl

@@ -26,6 +26,75 @@ end
     @test MOI.dimension(MOI.SOS2(collect(1:6))) === 6
 end
 
+@testset "Dual Set" begin
+    # Nonpositives
+    nonpositives3 = MOI.Nonpositives(3)
+    nonpositives4 = MOI.Nonpositives(4)
+    @test MOI.dual_set(nonpositives3) == nonpositives3
+    @test MOI.dual_set(nonpositives3) != nonpositives4
+    @test MOI.dual_set(nonpositives4) == nonpositives4
+    # Nonnegatives
+    nonnegatives3 = MOI.Nonnegatives(3)
+    nonnegatives4 = MOI.Nonnegatives(4)
+    @test MOI.dual_set(nonnegatives3) == nonnegatives3
+    @test MOI.dual_set(nonnegatives3) != nonnegatives4
+    @test MOI.dual_set(nonnegatives4) == nonnegatives4
+    # Zeros and Reals
+    zeros3 = MOI.Zeros(3)
+    zeros4 = MOI.Zeros(4)
+    reals3 = MOI.Reals(3)
+    reals4 = MOI.Reals(4)
+    @test MOI.dual_set(zeros3) == reals3
+    @test MOI.dual_set(reals3) == zeros3
+    @test MOI.dual_set(reals3) != zeros4
+    @test MOI.dual_set(zeros4) == reals4
+    @test MOI.dual_set(reals4) == zeros4
+    @test MOI.dual_set(zeros4) != reals3
+    #SOC
+    soc2 = MOI.SecondOrderCone(2)
+    soc3 = MOI.SecondOrderCone(3)
+    @test MOI.dual_set(soc2) == soc2
+    @test MOI.dual_set(soc2) != soc3
+    @test MOI.dual_set(soc3) == soc3
+    #RSOC
+    rsoc2 = MOI.RotatedSecondOrderCone(2)
+    rsoc3 = MOI.RotatedSecondOrderCone(3)
+    @test MOI.dual_set(rsoc2) == rsoc2
+    @test MOI.dual_set(rsoc2) != rsoc3
+    @test MOI.dual_set(rsoc3) == rsoc3
+    #PSDtriangle
+    psd2 = MOI.PositiveSemidefiniteConeTriangle(2)
+    psd3 = MOI.PositiveSemidefiniteConeTriangle(3)
+    @test MOI.dual_set(psd2) == psd2
+    @test MOI.dual_set(psd2) != psd3
+    @test MOI.dual_set(psd3) == psd3
+    # Exponential
+    exp = MOI.ExponentialCone()
+    dual_exp = MOI.DualExponentialCone()
+    @test MOI.dual_set(exp) == dual_exp
+    @test MOI.dual_set(exp) != exp
+    @test MOI.dual_set(dual_exp) == exp
+    @test MOI.dual_set(dual_exp) != dual_exp
+    # Power
+    pow03 = MOI.PowerCone(0.3)
+    pow04 = MOI.PowerCone(0.4)
+    dual_pow03 = MOI.DualPowerCone(0.3)
+    @test MOI.dual_set(pow03) == dual_pow03
+    @test MOI.dual_set(pow03) != pow03
+    @test MOI.dual_set(dual_pow03) == pow03
+    @test MOI.dual_set(dual_pow03) != pow04
+    @test MOI.dual_set(dual_pow03) != dual_pow03
+    # PSDSquare error
+    s = MOI.PositiveSemidefiniteConeSquare(4)
+    err = ErrorException("""Dual of $s is not defined in MathOptInterface.
+                            For more details see the comments in src/Bridges/Constraint/square.jl""")
+    @test_throws err MOI.dual_set(MOI.PositiveSemidefiniteConeSquare(4))
+    # Not implemented
+    s = MOI.LogDetConeTriangle(4)
+    err = ErrorException("Dual of $s is not implemented.")
+    @test_throws err MOI.dual_set(MOI.LogDetConeTriangle(4))
+end
+
 @testset "Set dot" begin
     vec = zeros(6)
     @test MOIU.set_dot(vec, vec, MOI.SecondOrderCone(6)) == 0
@@ -114,4 +183,4 @@ end
     @test MOIU. dot_coefficients(sp_vec, MOI.LogDetConeTriangle(3)) == sp_vec
     sp_vec[5] = 1
     @test MOIU.dot_coefficients(sp_vec, MOI.LogDetConeTriangle(3)) == sp_vec
-end
+end