Implement dual for Hermitian PSD cone (#2749)

Author: blegat

src/sets.jl

@@ -1352,6 +1352,12 @@ function dimension(set::HermitianPositiveSemidefiniteConeTriangle)
     return real_nnz + imag_nnz
 end
 
+dual_set(set::HermitianPositiveSemidefiniteConeTriangle) = set
+
+function dual_set_type(::Type{HermitianPositiveSemidefiniteConeTriangle})
+    return HermitianPositiveSemidefiniteConeTriangle
+end
+
 """
     side_dimension(
         set::Union{

test/General/sets.jl

@@ -275,6 +275,14 @@ function test_sets_dual_psdtriangle()
         MOI.ScaledPositiveSemidefiniteConeTriangle(2),
         MOI.ScaledPositiveSemidefiniteConeTriangle(3),
     )
+    _test_sets_dual_psdtriangle(
+        MOI.HermitianPositiveSemidefiniteConeTriangle(2),
+        MOI.HermitianPositiveSemidefiniteConeTriangle(3),
+    )
+    _test_sets_dual_psdtriangle(
+        MOI.Scaled(MOI.HermitianPositiveSemidefiniteConeTriangle(2)),
+        MOI.Scaled(MOI.HermitianPositiveSemidefiniteConeTriangle(3)),
+    )
     return
 end