Add support for Hermitian PSD in conic inequality (#3705)

src/macros/@constraint.jl

@@ -674,6 +674,12 @@ function _functionize(
     return LinearAlgebra.Symmetric(_functionize(v.data))
 end
 
+function _functionize(
+    v::LinearAlgebra.Hermitian{V},
+) where {V<:AbstractVariableRef}
+    return LinearAlgebra.Hermitian(_functionize(v.data))
+end
+
 _functionize(x) = x
 
 _functionize(::_MA.Zero) = false

src/sd.jl

@@ -774,6 +774,7 @@ function build_constraint(
         MOI.AbstractSymmetricMatrixSetTriangle,
         MOI.AbstractSymmetricMatrixSetSquare,
         PSDCone,
+        HermitianPSDCone,
     },
 )
     return build_constraint(error_fn, f, extra)
@@ -787,6 +788,7 @@ function build_constraint(
         MOI.AbstractSymmetricMatrixSetTriangle,
         MOI.AbstractSymmetricMatrixSetSquare,
         PSDCone,
+        HermitianPSDCone,
     },
 )
     new_f = _MA.operate!!(*, -1, f)

test/test_complex.jl

@@ -257,6 +257,23 @@ function test_complex_hermitian_constraint()
     return
 end
 
+function test_complex_hermitian_inequality_constraint()
+    model = Model()
+    @variable(model, x[1:2, 1:2])
+    H = LinearAlgebra.Hermitian(x)
+    @test vectorize(H, HermitianMatrixShape(2)) ==
+          [x[1, 1], x[1, 2], x[2, 2], 0.0]
+    @constraint(model, c, H >= 0, HermitianPSDCone())
+    @test constraint_object(c).func == [x[1, 1], x[1, 2], x[2, 2], 0.0]
+    @test function_string(MIME("text/plain"), constraint_object(c)) ==
+          "[x[1,1]  x[1,2];\n x[1,2]  x[2,2]]"
+    @constraint(model, c2, 0 <= H, HermitianPSDCone())
+    @test constraint_object(c2).func == [x[1, 1], x[1, 2], x[2, 2], 0.0]
+    @test function_string(MIME("text/plain"), constraint_object(c2)) ==
+          "[x[1,1]  x[1,2];\n x[1,2]  x[2,2]]"
+    return
+end
+
 function test_isreal()
     model = Model()
     @variable(model, x[1:2])