diff --git a/src/constrained_variables.jl b/src/constrained_variables.jl
index 4ecc19d..681a250 100644
--- a/src/constrained_variables.jl
+++ b/src/constrained_variables.jl
@@ -83,3 +83,16 @@ function _select_constrained_variables(
     end
     return
 end
+
+function _get_parameter_variables(::PrimalDualMap{T}, primal_model) where {T}
+    cis = MOI.get(
+        primal_model,
+        MOI.ListOfConstraintIndices{MOI.VariableIndex,MOI.Parameter{T}}(),
+    )
+    parameters = Set{MOI.VariableIndex}()
+    for ci in cis
+        vi = MOI.get(primal_model, MOI.ConstraintFunction(), ci)
+        push!(parameters, vi)
+    end
+    return parameters
+end
diff --git a/src/dual_equality_constraints.jl b/src/dual_equality_constraints.jl
index 6e68e20..098091a 100644
--- a/src/dual_equality_constraints.jl
+++ b/src/dual_equality_constraints.jl
@@ -410,6 +410,15 @@ function _fill_scalar_affine_terms!(
     return
 end
 
+function _fill_scalar_affine_terms!(
+    ::Dict{MOI.VariableIndex,Vector{MOI.ScalarAffineTerm{T}}},
+    primal_constraint_data,
+    ::MOI.ModelLike,
+    ::MOI.ConstraintIndex{MOI.VariableIndex,MOI.Parameter{T}},
+) where {T}
+    return
+end
+
 function _fill_scalar_affine_terms!(
     scalar_affine_terms::Dict{
         MOI.VariableIndex,
diff --git a/src/dual_model_variables.jl b/src/dual_model_variables.jl
index fe44042..ae3a589 100644
--- a/src/dual_model_variables.jl
+++ b/src/dual_model_variables.jl
@@ -10,8 +10,10 @@ function _add_dual_vars_in_dual_cones(
     primal_dual_map::PrimalDualMap{T},
     dual_names::DualNames,
     con_types::Vector{Tuple{Type,Type}},
+    variable_parameters,
 ) where {T}
     dual_obj_affine_terms = Dict{MOI.VariableIndex,T}()
+    parameters_set = Set(variable_parameters)
     for (F, S) in con_types
         _add_dual_vars_in_dual_cones(
             dual_obj_affine_terms,
@@ -21,6 +23,7 @@ function _add_dual_vars_in_dual_cones(
             dual_names,
             F,
             S,
+            parameters_set,
         )
     end
     return dual_obj_affine_terms
@@ -34,13 +37,22 @@ function _add_dual_vars_in_dual_cones(
     dual_names::DualNames,
     ::Type{F},
     ::Type{S},
+    parameters_set,
 ) where {T,F,S}
     for ci in MOI.get(primal_model, MOI.ListOfConstraintIndices{F,S}())
         # If `F` not one of these two, we can skip the `haskey` check.
-        if haskey(primal_dual_map.primal_constrained_variables, ci)
-            # primal constraints that are the main constraints of
-            # constrained variables have no dual variable associated
-            # bacause they associated with dual constraints
+        if haskey(primal_dual_map.primal_constrained_variables, ci) ||
+           # primal constraints that are the main constraints of
+           # constrained variables have no dual variable associated
+           # bacause they associated with dual constraints
+           (
+            F <: MOI.VariableIndex &&
+            MOI.get(primal_model, MOI.ConstraintFunction(), ci) in
+            parameters_set
+        )
+            # if a parameter is constrained, either because the set is
+            # Parameter or because it was user defined parameter its constraint
+            # will lead to a useless dual variable.
             continue
         end
         # Add dual variable to dual cone
diff --git a/src/dualize.jl b/src/dualize.jl
index 9c490c9..fcc8518 100644
--- a/src/dualize.jl
+++ b/src/dualize.jl
@@ -69,7 +69,7 @@ function dualize(
     primal_model::MOI.ModelLike,
     dual_problem::DualProblem{T},
     dual_names::DualNames,
-    variable_parameters::Vector{MOI.VariableIndex},
+    _variable_parameters::Vector{MOI.VariableIndex},
     ignore_objective::Bool,
     consider_constrained_variables::Bool,
 ) where {T}
@@ -80,6 +80,15 @@ function dualize(
     con_types = MOI.get(primal_model, MOI.ListOfConstraintTypesPresent())
     supported_constraints(con_types) # Errors if constraint cant be dualized
 
+    # merge user listed parameters and MOI.VariableIndex-in-MOI.Parameter{T}
+    moi_parameters =
+        _get_parameter_variables(dual_problem.primal_dual_map, primal_model)
+    all_parameters = Set{MOI.VariableIndex}(_variable_parameters)
+    for p in moi_parameters
+        push!(all_parameters, p)
+    end
+    variable_parameters = collect(all_parameters)
+
     # Set the dual model objective sense
     _set_dual_model_sense(dual_problem.dual_model, primal_model)
 
@@ -98,6 +107,8 @@ function dualize(
     # the respective primal variable will not be a constrained variable (with
     # respect to that constraint).
     # Constrained variables are registered in `primal_constrained_variables`.
+    # Since MOI.VariableIndex-in-MOI.Parameter{T} are in the variable_parameters
+    # list, they are not considered constrained variables, they are parameters.
     if consider_constrained_variables
         _select_constrained_variables(
             dual_problem,
@@ -132,6 +143,7 @@ function dualize(
         dual_problem.primal_dual_map,
         dual_names,
         con_types,
+        variable_parameters,
     )
 
     # Creates variables in the dual problem that represent parameters in the
diff --git a/src/supported.jl b/src/supported.jl
index eb2c62c..f87ca00 100644
--- a/src/supported.jl
+++ b/src/supported.jl
@@ -28,6 +28,13 @@ end
 
 supported_constraint(::Type, ::Type) = false
 
+function supported_constraint(
+    ::Type{MOI.VariableIndex},
+    S::Type{MOI.Parameter{T}},
+) where {T}
+    return true
+end
+
 function supported_constraint(
     ::Type{<:Union{MOI.VariableIndex,MOI.ScalarAffineFunction}},
     S::Type{<:MOI.AbstractScalarSet},
diff --git a/test/Tests/test_partial_dual_linear.jl b/test/Tests/test_partial_dual_linear.jl
index 20455cd..9a3a5db 100644
--- a/test/Tests/test_partial_dual_linear.jl
+++ b/test/Tests/test_partial_dual_linear.jl
@@ -106,14 +106,13 @@
         s.t.
             2x1 + x2 - 3 <= 0  :y_2
             x1 + 2x2 - 3 <= 0  :y_3
-            x1 >= 1            :y_1
+            x1 >= 1            :no dual here
             x2 >= 0
             ignore x_1 during dualization
         dual
             obj ignored
         s.t.
             -y_2 - 2y_3 >= 3 :x_2
-            y_1 >= 0
             y_2 <= 0
             y_3 <= 0
         =#
@@ -126,11 +125,10 @@
         dual_model = dual.dual_model
         primal_dual_map = dual.primal_dual_map
 
-        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 3
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 2
         list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
         @test Set(list_of_cons) == Set(
             [
-                (MOI.VariableIndex, MOI.GreaterThan{Float64})
                 (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64})
                 (MOI.VectorOfVariables, MOI.Nonpositives)
             ],
@@ -141,7 +139,7 @@
                 MOI.VariableIndex,
                 MOI.GreaterThan{Float64},
             }(),
-        ) == 1
+        ) == 0
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{MOI.VectorOfVariables,MOI.Nonpositives}(),
@@ -185,8 +183,7 @@
                 MOI.GreaterThan{Float64},
             }(),
         )
-        @test primal_constraint_data[vgt1].dual_variables ==
-              [MOI.VariableIndex(3)]
+        @test !haskey(primal_constraint_data, vgt1) # as this was not dualized
 
         for (vi, data) in primal_dual_map.primal_variable_data
             vi = MOI.VariableIndex(2)
@@ -203,7 +200,7 @@
             min 4x_3 + 5
         s.t.
             x_1 + 2x_2 + x_3 <= 20 :y_3
-            x_1 <= 1               :y_1
+            x_1 <= 1               : # no dual here: y_1
             x_2 <= 3               :y_2
         ignoring x_1 and x_3
         dual
@@ -212,7 +209,7 @@
             #  y_1 + y_3 == 0  :x_1
             y_2 + 2y_3 == 0 :x_2
             #  y_3 == 4.0      :x_3
-            y_1 <= 0
+            # y_1 <= 0
             y_2 <= 0
             y_3 <= 0
         =#
@@ -228,7 +225,7 @@
         dual_model = dual.dual_model
         primal_dual_map = dual.primal_dual_map
 
-        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 3
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 2
         list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
         @test Set(list_of_cons) == Set(
             [
@@ -239,7 +236,7 @@
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{MOI.VariableIndex,MOI.LessThan{Float64}}(),
-        ) == 3
+        ) == 2
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{
@@ -278,13 +275,118 @@
             MOI.LessThan{Float64},
         }(
             2,
-        )].dual_variables == [MOI.VariableIndex(3)]
+        )].dual_variables == [MOI.VariableIndex(2)]
+        @test !haskey(
+            primal_constraint_data,
+            MOI.ConstraintIndex{MOI.VariableIndex,MOI.LessThan{Float64}}(1),
+        )
         @test primal_constraint_data[MOI.ConstraintIndex{
-            MOI.VariableIndex,
+            MOI.ScalarAffineFunction{Float64},
             MOI.LessThan{Float64},
         }(
             1,
+        )].dual_variables == [MOI.VariableIndex(1)]
+
+        primal_variable_data = primal_dual_map.primal_variable_data
+        @test primal_variable_data[MOI.VariableIndex(2)].dual_constraint ==
+              MOI.ConstraintIndex{
+            MOI.ScalarAffineFunction{Float64},
+            MOI.EqualTo{Float64},
+        }(
+            1,
+        )
+    end
+
+    @testset "lp12_test - x_1 ignored x_3 moi_param" begin
+        #=
+        primal
+            min 4x_3 + 5
+        s.t.
+            x_1 + 2x_2 + x_3 <= 20 :y_3
+            x_1 <= 1               : # no dual here: y_1
+            x_2 <= 3               :y_2
+        ignoring x_1 and x_3
+        dual
+            obj ignored
+        s.t.
+            #  y_1 + y_3 == 0  :x_1
+            y_2 + 2y_3 == 0 :x_2
+            #  y_3 == 4.0      :x_3
+            # y_1 <= 0
+            y_2 <= 0
+            y_3 <= 0
+        =#
+        primal_model = lp12_test()
+        MOI.add_constraint(
+            primal_model,
+            MOI.VariableIndex(3),
+            MOI.Parameter{Float64}(0.0),
+        )
+        dual = Dualization.dualize(
+            primal_model,
+            variable_parameters = MOI.VariableIndex[MOI.VariableIndex(1),
+            # MOI.VariableIndex(3), # as a param
+            ],
+            ignore_objective = true,
+        )
+        dual_model = dual.dual_model
+        primal_dual_map = dual.primal_dual_map
+
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 2
+        list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
+        @test Set(list_of_cons) == Set(
+            [
+                (MOI.VariableIndex, MOI.LessThan{Float64})
+                (MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64})
+            ],
+        )
+        @test MOI.get(
+            dual_model,
+            MOI.NumberOfConstraints{MOI.VariableIndex,MOI.LessThan{Float64}}(),
+        ) == 2
+        @test MOI.get(
+            dual_model,
+            MOI.NumberOfConstraints{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(),
+        ) == 1
+
+        eq_con2_fun = MOI.get(
+            dual_model,
+            MOI.ConstraintFunction(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                1,
+            ),
+        )
+        eq_con2_set = MOI.get(
+            dual_model,
+            MOI.ConstraintSet(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                1,
+            ),
+        )
+        @test MOI.coefficient.(eq_con2_fun.terms) == [2.0; 1.0]
+        @test MOI.constant.(eq_con2_fun) == 0.0
+        @test MOI.constant(eq_con2_set) == 0.0
+
+        primal_constraint_data = primal_dual_map.primal_constraint_data
+        @test primal_constraint_data[MOI.ConstraintIndex{
+            MOI.VariableIndex,
+            MOI.LessThan{Float64},
+        }(
+            2,
         )].dual_variables == [MOI.VariableIndex(2)]
+        @test !haskey(
+            primal_constraint_data,
+            MOI.ConstraintIndex{MOI.VariableIndex,MOI.LessThan{Float64}}(1),
+        )
         @test primal_constraint_data[MOI.ConstraintIndex{
             MOI.ScalarAffineFunction{Float64},
             MOI.LessThan{Float64},
diff --git a/test/Tests/test_partial_dual_quadratic.jl b/test/Tests/test_partial_dual_quadratic.jl
index 9621345..a064570 100644
--- a/test/Tests/test_partial_dual_quadratic.jl
+++ b/test/Tests/test_partial_dual_quadratic.jl
@@ -147,35 +147,40 @@
         @test primal_var_in_quad_obj_to_dual_slack_var[MOI.VariableIndex(2)] ==
               MOI.VariableIndex(2 + 1 + 2)
     end
-    @testset "qp2_test - ignore y" begin
+    @testset "qp1_test - z moi_param" begin
         #=
-            min 2 x^2 + y^2 + xy + x + y + 1
+            min x^2 + xy + y^2 + yz + z^2
         s.t.
-            x + y = 1 (a)
-            x    >= 0 (b)
-               y >= 0 (c)
+            x + 2y + 3z >= 4 (a)
+            x +  y      >= 1 (b)
+            x,y,z \in R
         dual
-            max 1 + y + a - y a - y c - 2 w1^2 + y^2
+            max 4a - 3z a +  b - w1^2 - w1 w2 - w2^2 + z^2
         s.t.
-            - a - b     + y + 4w1 + 1 = 0
-            a \in R
+            - a -  b + 2 w1 + 1 w2     = 0
+            -2a -  b + 1 w1 + 2 w2 + z = 0
+            a >= 0
             b >= 0
-            c >= 0
         =#
-        primal_model = qp2_test()
+        primal_model = qp1_test()
+        MOI.add_constraint(
+            primal_model,
+            MOI.VariableIndex(3),
+            MOI.Parameter{Float64}(1.0),
+        )
         dual = Dualization.dualize(
             primal_model,
-            variable_parameters = MOI.VariableIndex[MOI.VariableIndex(2)],
+            # variable_parameters = MOI.VariableIndex[MOI.VariableIndex(3)],
         )
         dual_model = dual.dual_model
         primal_dual_map = dual.primal_dual_map
 
-        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 4
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 2 + 2 + 1
         list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
         @test Set(list_of_cons) == Set(
             [
                 (MOI.VariableIndex, MOI.GreaterThan{Float64})
-                (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64})
+                (MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64})
             ],
         )
         @test MOI.get(
@@ -184,7 +189,149 @@
                 MOI.VariableIndex,
                 MOI.GreaterThan{Float64},
             }(),
-        ) == 1
+        ) == 2
+        @test MOI.get(
+            dual_model,
+            MOI.NumberOfConstraints{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(),
+        ) == 2
+        obj_type = MOI.get(dual_model, MOI.ObjectiveFunctionType())
+        @test obj_type == MOI.ScalarQuadraticFunction{Float64}
+        obj = MOI.get(dual_model, MOI.ObjectiveFunction{obj_type}())
+        @test MOI.constant(obj) == 0.0
+        @test MOI.coefficient.(obj.affine_terms) == [1.0; 4.0]
+        @test MOI.coefficient.(obj.quadratic_terms) ==
+              [-2.0; -1.0; -2.0; 2.0; -3.0]
+
+        eq_con1_fun = MOI.get(
+            dual_model,
+            MOI.ConstraintFunction(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                1,
+            ),
+        )
+        eq_con1_set = MOI.get(
+            dual_model,
+            MOI.ConstraintSet(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                1,
+            ),
+        )
+        @test MOI.coefficient.(eq_con1_fun.terms) == [1.0; 1.0; -2.0; -1.0]
+        @test MOI.constant.(eq_con1_fun) == 0.0
+        @test MOI.constant(eq_con1_set) == 0.0
+        eq_con2_fun = MOI.get(
+            dual_model,
+            MOI.ConstraintFunction(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                2,
+            ),
+        )
+        eq_con2_set = MOI.get(
+            dual_model,
+            MOI.ConstraintSet(),
+            MOI.ConstraintIndex{
+                MOI.ScalarAffineFunction{Float64},
+                MOI.EqualTo{Float64},
+            }(
+                2,
+            ),
+        )
+        @test MOI.coefficient.(eq_con2_fun.terms) ==
+              [2.0; 1.0; -1.0; -1.0; -2.0]
+        @test MOI.constant.(eq_con2_fun) == 0.0
+        @test MOI.constant(eq_con2_set) == 0.0
+
+        primal_constraint_data = primal_dual_map.primal_constraint_data
+        @test primal_constraint_data[MOI.ConstraintIndex{
+            MOI.ScalarAffineFunction{Float64},
+            MOI.GreaterThan{Float64},
+        }(
+            1,
+        )].dual_variables == [MOI.VariableIndex(1)]
+        @test primal_constraint_data[MOI.ConstraintIndex{
+            MOI.ScalarAffineFunction{Float64},
+            MOI.GreaterThan{Float64},
+        }(
+            2,
+        )].dual_variables == [MOI.VariableIndex(2)]
+
+        primal_variable_data = primal_dual_map.primal_variable_data
+        @test primal_variable_data[MOI.VariableIndex(1)].dual_constraint ==
+              MOI.ConstraintIndex{
+            MOI.ScalarAffineFunction{Float64},
+            MOI.EqualTo{Float64},
+        }(
+            1,
+        )
+        @test primal_variable_data[MOI.VariableIndex(2)].dual_constraint ==
+              MOI.ConstraintIndex{
+            MOI.ScalarAffineFunction{Float64},
+            MOI.EqualTo{Float64},
+        }(
+            2,
+        )
+
+        primal_parameter_to_dual_parameter =
+            primal_dual_map.primal_parameter_to_dual_parameter
+        @test primal_parameter_to_dual_parameter[MOI.VariableIndex(3)] ==
+              MOI.VariableIndex(2 + 1)
+
+        primal_var_in_quad_obj_to_dual_slack_var =
+            primal_dual_map.primal_var_in_quad_obj_to_dual_slack_var
+        @test primal_var_in_quad_obj_to_dual_slack_var[MOI.VariableIndex(1)] ==
+              MOI.VariableIndex(2 + 1 + 1)
+        @test primal_var_in_quad_obj_to_dual_slack_var[MOI.VariableIndex(2)] ==
+              MOI.VariableIndex(2 + 1 + 2)
+    end
+    @testset "qp2_test - ignore y" begin
+        #=
+            min 2 x^2 + y^2 + xy + x + y + 1
+        s.t.
+            x + y = 1 (a)
+            x    >= 0 (b) # no dual becaus is interpreted as a constrainted var
+               y >= 0 (c) # ignored so no dual
+        dual
+            # max 1 + y + a - y a - y c - 2 w1^2 + y^2
+            max 1 + y + a - y a - 2 w1^2 + y^2
+        s.t.
+            - a - b     + y + 4w1 + 1 = 0 # - a     + y + 4w1 + 1 >= 0
+            a \in R
+            # b >= 0 # does no exist as is a constrained variable con
+            # c >= 0 # ignored so no dual
+        =#
+        primal_model = qp2_test()
+        dual = Dualization.dualize(
+            primal_model,
+            variable_parameters = MOI.VariableIndex[MOI.VariableIndex(2)],
+        )
+        dual_model = dual.dual_model
+        primal_dual_map = dual.primal_dual_map
+
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 3
+        list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
+        @test Set(list_of_cons) == Set([(
+            MOI.ScalarAffineFunction{Float64},
+            MOI.GreaterThan{Float64},
+        )],)
+        @test MOI.get(
+            dual_model,
+            MOI.NumberOfConstraints{
+                MOI.VariableIndex,
+                MOI.GreaterThan{Float64},
+            }(),
+        ) == 0
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{
@@ -197,7 +344,7 @@
         obj = MOI.get(dual_model, MOI.ObjectiveFunction{obj_type}())
         @test MOI.constant(obj) == 1.0
         @test MOI.coefficient.(obj.affine_terms) == [1.0; 1.0]
-        @test MOI.coefficient.(obj.quadratic_terms) == [-4.0; 2.0; -1.0; -1.0]
+        @test MOI.coefficient.(obj.quadratic_terms) == [-4.0; 2.0; -1.0]
 
         eq_con1_fun = MOI.get(
             dual_model,
@@ -234,12 +381,10 @@
             primal_constraint_data,
             MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{Float64}}(1),
         )
-        @test primal_constraint_data[MOI.ConstraintIndex{
-            MOI.VariableIndex,
-            MOI.GreaterThan{Float64},
-        }(
-            2,
-        )].dual_variables == [MOI.VariableIndex(2)]
+        @test !haskey(
+            primal_constraint_data,
+            MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{Float64}}(2),
+        )
 
         for (vi, data) in primal_dual_map.primal_variable_data
             @test vi == MOI.VariableIndex(1)
@@ -258,12 +403,12 @@
         primal_parameter_to_dual_parameter =
             primal_dual_map.primal_parameter_to_dual_parameter
         @test primal_parameter_to_dual_parameter[MOI.VariableIndex(2)] ==
-              MOI.VariableIndex(3)
+              MOI.VariableIndex(2)
 
         primal_var_in_quad_obj_to_dual_slack_var =
             primal_dual_map.primal_var_in_quad_obj_to_dual_slack_var
         @test primal_var_in_quad_obj_to_dual_slack_var[MOI.VariableIndex(1)] ==
-              MOI.VariableIndex(4)
+              MOI.VariableIndex(3)
     end
     @testset "qp2_test - ignore y - no obj" begin
         #=
@@ -289,21 +434,19 @@
         dual_model = dual.dual_model
         primal_dual_map = dual.primal_dual_map
 
-        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 4
+        @test MOI.get(dual_model, MOI.NumberOfVariables()) == 3
         list_of_cons = MOI.get(dual_model, MOI.ListOfConstraintTypesPresent())
-        @test Set(list_of_cons) == Set(
-            [
-                (MOI.VariableIndex, MOI.GreaterThan{Float64})
-                (MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64})
-            ],
-        )
+        @test Set(list_of_cons) == Set([(
+            MOI.ScalarAffineFunction{Float64},
+            MOI.GreaterThan{Float64},
+        )],)
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{
                 MOI.VariableIndex,
                 MOI.GreaterThan{Float64},
             }(),
-        ) == 1
+        ) == 0
         @test MOI.get(
             dual_model,
             MOI.NumberOfConstraints{
@@ -352,12 +495,10 @@
             primal_constraint_data,
             MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{Float64}}(1),
         ))
-        @test primal_constraint_data[MOI.ConstraintIndex{
-            MOI.VariableIndex,
-            MOI.GreaterThan{Float64},
-        }(
-            2,
-        )].dual_variables == [MOI.VariableIndex(2)]
+        @test !haskey(
+            primal_constraint_data,
+            MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{Float64}}(2),
+        )
 
         for (vi, data) in primal_dual_map.primal_variable_data
             @test vi == MOI.VariableIndex(1)
@@ -376,11 +517,11 @@
         primal_parameter_to_dual_parameter =
             primal_dual_map.primal_parameter_to_dual_parameter
         @test primal_parameter_to_dual_parameter[MOI.VariableIndex(2)] ==
-              MOI.VariableIndex(3)
+              MOI.VariableIndex(2)
 
         primal_var_in_quad_obj_to_dual_slack_var =
             primal_dual_map.primal_var_in_quad_obj_to_dual_slack_var
         @test primal_var_in_quad_obj_to_dual_slack_var[MOI.VariableIndex(1)] ==
-              MOI.VariableIndex(4)
+              MOI.VariableIndex(3)
     end
 end