diff --git a/src/sets.jl b/src/sets.jl
index a5361684c7..8acb9d6bdb 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -1852,8 +1852,19 @@ MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInte
 """
 struct SOS1{T<:Real} <: AbstractVectorSet
     weights::Vector{T}
+
+    function SOS1{T}(weights::Vector{T}) where {T<:Real}
+        if isempty(weights)
+            throw(DimensionMismatch("Dimension of SOS1 must be > 0."))
+        end
+        return new{T}(weights)
+    end
 end
 
+SOS1(w::AbstractVector{T}) where {T<:Real} = SOS1{T}(w)
+
+SOS1{T}(w::AbstractVector) where {T<:Real} = SOS1{T}(convert(Vector{T}, w))
+
 dimension(set::SOS1) = length(set.weights)
 
 Base.copy(set::SOS1{T}) where {T} = SOS1{T}(copy(set.weights))
@@ -1889,8 +1900,19 @@ MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInte
 """
 struct SOS2{T<:Real} <: AbstractVectorSet
     weights::Vector{T}
+
+    function SOS2{T}(weights::Vector{T}) where {T<:Real}
+        if isempty(weights)
+            throw(DimensionMismatch("Dimension of SOS2 must be > 0."))
+        end
+        return new{T}(weights)
+    end
 end
 
+SOS2(w::AbstractVector{T}) where {T<:Real} = SOS2{T}(w)
+
+SOS2{T}(w::AbstractVector) where {T<:Real} = SOS2{T}(convert(Vector{T}, w))
+
 dimension(set::SOS2) = length(set.weights)
 
 Base.copy(set::SOS2{T}) where {T} = SOS2{T}(copy(set.weights))
diff --git a/test/General/test_sets.jl b/test/General/test_sets.jl
index 853dc97eda..9947beb384 100644
--- a/test/General/test_sets.jl
+++ b/test/General/test_sets.jl
@@ -503,6 +503,24 @@ function test_VectorNonlinearOracle()
     return
 end
 
+function test_SOS1_constructor()
+    @test_throws DimensionMismatch MOI.SOS1{Float64}(Float64[])
+    @test_throws DimensionMismatch MOI.SOS1(Float64[])
+    @test_throws DimensionMismatch MOI.SOS1(1:0)
+    @test MOI.SOS1(1:3) == MOI.SOS1{Int}(Int[1, 2, 3])
+    @test MOI.SOS1{Float64}(1:3) == MOI.SOS1{Float64}([1.0, 2.0, 3.0])
+    return
+end
+
+function test_SOS2_constructor()
+    @test_throws DimensionMismatch MOI.SOS2{Float64}(Float64[])
+    @test_throws DimensionMismatch MOI.SOS2(Float64[])
+    @test_throws DimensionMismatch MOI.SOS2(1:0)
+    @test MOI.SOS2(1:3) == MOI.SOS2{Int}(Int[1, 2, 3])
+    @test MOI.SOS2{Float64}(1:3) == MOI.SOS2{Float64}([1.0, 2.0, 3.0])
+    return
+end
+
 end  # module
 
 TestSets.runtests()