diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index b66918fe..37487402 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -1,7 +1,14 @@
 name: CI
 on:
-  - push
-  - pull_request
+  push:
+    branches:
+      - master
+  pull_request:
+    types: [opened, synchronize, reopened]
+# needed to allow julia-actions/cache to delete old caches that it has created
+permissions:
+  actions: write
+  contents: read
 jobs:
   test:
     name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
@@ -17,21 +24,12 @@ jobs:
             os: windows-latest
             arch: x64
     steps:
-      - uses: actions/checkout@v3
-      - uses: julia-actions/setup-julia@v1
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
-      - uses: actions/cache@v3
-        env:
-          cache-name: cache-artifacts
-        with:
-          path: ~/.julia/artifacts
-          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
-          restore-keys: |
-            ${{ runner.os }}-test-${{ env.cache-name }}-
-            ${{ runner.os }}-test-
-            ${{ runner.os }}-
+      - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
         env:
@@ -48,23 +46,17 @@ jobs:
       # Fix for Plots with GR backend, see https://github.com/jheinen/GR.jl/issues/422
       GKSwstype: nul
     steps:
-      - uses: actions/checkout@v3
-      - uses: julia-actions/setup-julia@v1
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
         with:
           version: '1'
-      - shell: bash
-        run: julia --project=docs -e "using Pkg; Pkg.develop(PackageSpec(path=pwd()))"
-      - shell: bash
-        run: julia --project=docs -e "using Pkg; Pkg.instantiate()"
-      - shell: bash
-        env:
-          DATADEPS_ALWAYS_ACCEPT: true # For MLDatasets.MNIST
+      - name: Install dependencies
+        shell: julia --color=yes --project=docs/ {0}
         run: |
-          julia --project=docs -e '
-            using Documenter: doctest
-            using DiffOpt
-            doctest(DiffOpt)'
-      - run: julia --project=docs docs/make.jl
+          using Pkg
+          Pkg.develop(PackageSpec(path=pwd()))
+          Pkg.instantiate()
+      - run: julia --project=docs --color=yes docs/make.jl
         env:
           DATADEPS_ALWAYS_ACCEPT: true # For MLDatasets.MNIST
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
diff --git a/Project.toml b/Project.toml
index a3689608..e89e4c6b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -23,5 +23,5 @@ JuMP = "1"
 LazyArrays = "0.21, 0.22, 1"
 MathOptInterface = "1.18"
 MathOptSetDistances = "0.2.9"
-ParametricOptInterface = "0.9.0"
+ParametricOptInterface = "0.11"
 julia = "1.6"
diff --git a/docs/Project.toml b/docs/Project.toml
index f953f3b3..c4112c75 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -15,4 +15,4 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-Documenter = "0.27"
+Documenter = "1"
diff --git a/docs/make.jl b/docs/make.jl
index 9d825aaf..a31f7e28 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -43,8 +43,10 @@ end
 literate_directory(_EXAMPLE_DIR)
 
 makedocs(;
+    authors = "JuMP Community",
+    sitename = "DiffOpt.jl",
+    repo = "https://github.com/jump-dev/DiffOpt.jl",
     modules = [DiffOpt],
-    doctest = false,
     clean = true,
     format = Documenter.HTML(;
         prettyurls = get(ENV, "CI", nothing) == "true",
@@ -61,10 +63,6 @@ makedocs(;
             f in readdir(_EXAMPLE_DIR) if endswith(f, ".md")
         ],
     ],
-    strict = true,  # See https://github.com/JuliaOpt/JuMP.jl/issues/1576
-    repo = "https://github.com/jump-dev/DiffOpt.jl",
-    sitename = "DiffOpt.jl",
-    authors = "JuMP Community",
 )
 
 deploydocs(; repo = "github.com/jump-dev/DiffOpt.jl.git", push_preview = true)
diff --git a/src/ConicProgram/ConicProgram.jl b/src/ConicProgram/ConicProgram.jl
index 89a79183..f9444404 100644
--- a/src/ConicProgram/ConicProgram.jl
+++ b/src/ConicProgram/ConicProgram.jl
@@ -302,6 +302,7 @@ function DiffOpt.forward_differentiate!(model::Model)
             dAj,
             dAv,
         )
+        dAv .*= -1.0
         dA = SparseArrays.sparse(dAi, dAj, dAv, lines, cols)
 
         m = size(A, 1)
diff --git a/src/bridges.jl b/src/bridges.jl
index 2b0eb46b..a56717b3 100644
--- a/src/bridges.jl
+++ b/src/bridges.jl
@@ -3,6 +3,30 @@
 # Use of this source code is governed by an MIT-style license that can be found
 # in the LICENSE.md file or at https://opensource.org/licenses/MIT.
 
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::ObjectiveFunctionAttribute{ReverseObjectiveFunction,G},
+    ::MOI.Bridges.Objective.FunctionConversionBridge{T,F,G},
+) where {T,F,G}
+    return MOI.get(
+        model,
+        ObjectiveFunctionAttribute{ReverseObjectiveFunction,F}(attr.attr),
+    )
+end
+
+function MOI.set(
+    model::MOI.ModelLike,
+    attr::ObjectiveFunctionAttribute{ForwardObjectiveFunction,G},
+    ::MOI.Bridges.Objective.FunctionConversionBridge{T,F,G},
+    value,
+) where {T,F,G}
+    return MOI.set(
+        model,
+        ObjectiveFunctionAttribute{ForwardObjectiveFunction,F}(attr.attr),
+        value,
+    )
+end
+
 function MOI.get(
     model::MOI.ModelLike,
     ::ObjectiveFunctionAttribute{ReverseObjectiveFunction},
diff --git a/test/conic_program.jl b/test/conic_program.jl
index a3d4a939..f5e5b000 100644
--- a/test/conic_program.jl
+++ b/test/conic_program.jl
@@ -11,6 +11,7 @@ import Ipopt
 import LinearAlgebra
 import MathOptInterface as MOI
 import SCS
+using JuMP
 
 const ATOL = 2e-4
 const RTOL = 2e-4
@@ -28,7 +29,7 @@ end
 
 function _test_simple_socp(eq_vec::Bool)
     # referred from _soc2test, https://github.com/jump-dev/MathOptInterface.jl/blob/master/src/Test/contconic.jl#L1355
-    # find equivalent diffcp python program here: https://github.com/AKS1996/jump-gsoc-2020/blob/master/diffcp_socp_1_py.ipynb
+    # find reference diffcp python program here: https://github.com/AKS1996/jump-gsoc-2020/blob/master/diffcp_socp_1_py.ipynb
     # Problem SOC2
     # min  x
     # s.t. y ≥ 1/√2
@@ -38,80 +39,103 @@ function _test_simple_socp(eq_vec::Bool)
     # s.t.  -1/√2 + y ∈ R₊
     #        1 - t ∈ {0}
     #      (t,x,y) ∈ SOC₃
-    model = DiffOpt.diff_optimizer(SCS.Optimizer)
-    MOI.set(model, MOI.Silent(), true)
-    x, y, t = MOI.add_variables(model, 3)
-    MOI.set(
-        model,
-        MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
-        1.0x,
-    )
-    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+
+    model = JuMP.Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
+    set_silent(model)
+
+    x = @variable(model)
+    y = @variable(model)
+    t = @variable(model)
+
+    ceq = if eq_vec
+        @constraint(model, [t] .== [1.0])
+    else
+        @constraint(model, t == 1.0)
+    end
+    cnon = @constraint(model, 1.0y >= 1 / √2)
+    csoc = @constraint(model, [1.0t, 1.0x, 1.0y] in MOI.SecondOrderCone(3))
+
+    @objective(model, Min, 1.0x)
+
+    optimize!(model)
+
+    # set foward sensitivities
     if eq_vec
-        ceq = MOI.add_constraint(
-            model,
-            MOI.Utilities.vectorize([-1.0t + 1.0]),
-            MOI.Zeros(1),
-        )
+        MOI.set.(model, DiffOpt.ForwardConstraintFunction(), ceq, [1.0 * x])
     else
-        ceq = MOI.add_constraint(model, -1.0t, MOI.EqualTo(-1.0))
+        MOI.set(model, DiffOpt.ForwardConstraintFunction(), ceq, 1.0 * x)
     end
-    cnon = MOI.add_constraint(
-        model,
-        MOI.Utilities.vectorize([1.0y - 1 / √2]),
-        MOI.Nonnegatives(1),
-    )
-    csoc = MOI.add_constraint(
-        model,
-        MOI.Utilities.vectorize([1.0t, 1.0x, 1.0y]),
-        MOI.SecondOrderCone(3),
-    )
-    MOI.optimize!(model)
+
+    DiffOpt.forward_differentiate!(model)
+
+    dx = -0.9999908
+    @test MOI.get(model, DiffOpt.ForwardVariablePrimal(), x) ≈ dx atol = ATOL rtol =
+        RTOL
+
+    MOI.set(model, DiffOpt.ReverseVariablePrimal(), x, 1.0)
+
+    DiffOpt.reverse_differentiate!(model)
+
     if eq_vec
-        MOI.set(
-            model,
-            DiffOpt.ForwardConstraintFunction(),
-            ceq,
-            MOI.Utilities.vectorize([1.0 * x]),
+        @test all(
+            isapprox.(
+                JuMP.coefficient.(
+                    MOI.get.(model, DiffOpt.ReverseConstraintFunction(), ceq),
+                    x,
+                ),
+                dx,
+                atol = ATOL,
+                rtol = RTOL,
+            ),
         )
     else
-        MOI.set(model, DiffOpt.ForwardConstraintFunction(), ceq, 1.0 * x)
+        @test JuMP.coefficient(
+            MOI.get(model, DiffOpt.ReverseConstraintFunction(), ceq),
+            x,
+        ) ≈ dx atol = ATOL rtol = RTOL
     end
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        cnon,
-        MOI.Utilities.vectorize([1.0 * y]),
-    )
+
+    DiffOpt.empty_input_sensitivities!(model)
+
+    MOI.set(model, DiffOpt.ForwardConstraintFunction(), cnon, 1.0 * y)
+
+    DiffOpt.forward_differentiate!(model)
+
+    dy = -0.707083
+    @test MOI.get(model, DiffOpt.ForwardVariablePrimal(), y) ≈ dy atol = ATOL rtol =
+        RTOL
+
+    MOI.set(model, DiffOpt.ReverseVariablePrimal(), y, 1.0)
+
+    DiffOpt.reverse_differentiate!(model)
+
+    @test JuMP.coefficient(
+        MOI.get(model, DiffOpt.ReverseConstraintFunction(), cnon),
+        y,
+    ) ≈ dy atol = ATOL rtol = RTOL
+
+    DiffOpt.empty_input_sensitivities!(model)
+
     MOI.set(
         model,
         DiffOpt.ForwardConstraintFunction(),
         csoc,
-        MOI.Utilities.operate(vcat, Float64, 1.0 * t, 0.0, 0.0),
+        MOI.Utilities.operate(vcat, Float64, 1.0 * t.index, 0.0, 0.0),
     )
+
     DiffOpt.forward_differentiate!(model)
-    # these matrices are benchmarked with the output generated by diffcp
-    # refer the python file mentioned above to get equivalent python source code
-    @test model.diff.model.x ≈ [-1 / √2; 1 / √2; 1.0] atol = ATOL rtol = RTOL
-    if eq_vec
-        @test model.diff.model.s ≈ [0.0, 0.0, 1.0, -1 / √2, 1 / √2] atol = ATOL rtol =
-            RTOL
-        @test model.diff.model.y ≈ [√2, 1.0, √2, 1.0, -1.0] atol = ATOL rtol =
-            RTOL
-    else
-        @test model.diff.model.s ≈ [0.0, 1.0, -1 / √2, 1 / √2, 0.0] atol = ATOL rtol =
-            RTOL
-        @test model.diff.model.y ≈ [1.0, √2, 1.0, -1.0, √2] atol = ATOL rtol =
-            RTOL
-    end
-    dx = [1.12132144; 1 / √2; 1 / √2]
-    for (i, vi) in enumerate([x, y, t])
-        @test dx[i] ≈ MOI.get(model, DiffOpt.ForwardVariablePrimal(), vi) atol =
-            ATOL rtol = RTOL
-    end
-    # @test dx ≈ [1.12132144; 1/√2; 1/√2] atol=ATOL rtol=RTOL
-    # @test ds ≈ [0.0; 0.0; -2.92893438e-01;  1.12132144e+00; 7.07106999e-01]  atol=ATOL rtol=RTOL
-    # @test dy ≈ [2.4142175; 5.00000557; 3.8284315; √2; -4.00000495] atol=ATOL rtol=RTOL
+
+    ds = 0.0
+    @test MOI.get(model, DiffOpt.ForwardVariablePrimal(), t) ≈ ds atol = ATOL rtol =
+        RTOL
+
+    MOI.set(model, DiffOpt.ReverseVariablePrimal(), t, 1.0)
+
+    DiffOpt.reverse_differentiate!(model)
+
+    # FIXME: this is not working - https://github.com/jump-dev/DiffOpt.jl/issues/283
+    # @test JuMP.coefficient(MOI.get(model, DiffOpt.ReverseConstraintFunction(), csoc).func.func.func, t.index) ≈ ds atol=ATOL rtol=RTOL
+
     return
 end
 
@@ -375,206 +399,82 @@ function test_differentiating_conic_with_PSD_and_SOC_constraints()
     return
 end
 
-function test_differentiating_conic_with_PSD_and_POS_constraints()
+function _build_simple_sdp()
     # refer psdt2test, https://github.com/jump-dev/MathOptInterface.jl/blob/master/src/Test/contconic.jl#L4306
     # find equivalent diffcp program here - https://github.com/AKS1996/jump-gsoc-2020/blob/master/diffcp_sdp_3_py.ipynb
-    model = DiffOpt.diff_optimizer(SCS.Optimizer)
-    MOI.set(model, MOI.Silent(), true)
-    x = MOI.add_variables(model, 7)
-    @test MOI.get(model, MOI.NumberOfVariables()) == 7
-    η = 10.0
-    c1 = MOI.add_constraint(
-        model,
-        MOI.VectorAffineFunction(
-            MOI.VectorAffineTerm.(1, MOI.ScalarAffineTerm.(-1.0, x[1:6])),
-            [η],
-        ),
-        MOI.Nonnegatives(1),
-    )
-    c2 = MOI.add_constraint(
-        model,
-        MOI.VectorAffineFunction(
-            MOI.VectorAffineTerm.(1:6, MOI.ScalarAffineTerm.(1.0, x[1:6])),
-            zeros(6),
-        ),
-        MOI.Nonnegatives(6),
-    )
-    α = 0.8
-    δ = 0.9
-    c3 = MOI.add_constraint(
-        model,
-        MOI.VectorAffineFunction(
-            MOI.VectorAffineTerm.(
-                [fill(1, 7); fill(2, 5); fill(3, 6)],
-                MOI.ScalarAffineTerm.(
-                    [
-                        δ / 2,
-                        α,
-                        δ,
-                        δ / 4,
-                        δ / 8,
-                        0.0,
-                        -1.0,
-                        -δ / (2 * √2),
-                        -δ / 4,
-                        0,
-                        -δ / (8 * √2),
-                        0.0,
-                        δ / 2,
-                        δ - α,
-                        0,
-                        δ / 8,
-                        δ / 4,
-                        -1.0,
-                    ],
-                    [x[1:7]; x[1:3]; x[5:6]; x[1:3]; x[5:7]],
-                ),
-            ),
-            zeros(3),
-        ),
-        MOI.PositiveSemidefiniteConeTriangle(2),
-    )
-    c4 = MOI.add_constraint(
-        model,
-        MOI.VectorAffineFunction(
-            MOI.VectorAffineTerm.(
-                1,
-                MOI.ScalarAffineTerm.(0.0, [x[1:3]; x[5:6]]),
-            ),
-            [0.0],
-        ),
-        MOI.Zeros(1),
-    )
-    MOI.set(
-        model,
-        MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
-        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x[7])], 0.0),
-    )
-    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-    MOI.optimize!(model)
-    # dc = ones(7)
-    MOI.set(
-        model,
-        DiffOpt.ForwardObjectiveFunction(),
-        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(ones(7), x), 0.0),
-    )
-    # db = ones(11)
-    # dA = ones(11, 7)
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c1,
-        MOI.Utilities.vectorize(ones(1, 7) * x + ones(1)),
-    )
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c2,
-        MOI.Utilities.vectorize(ones(6, 7) * x + ones(6)),
-    )
-    MOI.set(
+    # Make a JuMP model backed by DiffOpt.diff_optimizer(SCS.Optimizer)
+    model = Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
+    set_silent(model)  # just to suppress solver output
+
+    @variable(model, x[1:3])
+
+    @constraint(model, c1, sum(x[i] for i in 1:3) == 4)
+
+    @constraint(model, c2[i = 1:3], x[i] ≥ 0)
+
+    @constraint(model, x[1] == 2)
+
+    @constraint(
         model,
-        DiffOpt.ForwardConstraintFunction(),
         c3,
-        MOI.Utilities.vectorize(ones(3, 7) * x + ones(3)),
-    )
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c4,
-        MOI.Utilities.vectorize(ones(1, 7) * x + ones(1)),
+        LinearAlgebra.Symmetric([
+            x[3]+1 2
+            2 2x[3]+2
+        ]) in PSDCone()
     )
-    DiffOpt.forward_differentiate!(model)
-    @test model.diff.model.x ≈
-          [20 / 3.0, 0.0, 10 / 3.0, 0.0, 0.0, 0.0, 1.90192379] atol = ATOL rtol =
-        RTOL
-    @test model.diff.model.s ≈ [
-        0.0,
-        0.0,
-        20 / 3.0,
-        0.0,
-        10 / 3.0,
-        0.0,
-        0.0,
-        0.0,
-        4.09807621,
-        -2.12132,
-        1.09807621,
-    ] atol = ATOL rtol = RTOL
-    @test model.diff.model.y ≈ [
-        0.0,
-        0.19019238,
-        0.0,
-        0.12597667,
-        0.0,
-        0.14264428,
-        0.14264428,
-        0.01274047,
-        0.21132487,
-        0.408248,
-        0.78867513,
-    ] atol = ATOL rtol = RTOL
-    atol = 0.3
-    rtol = 0.01
-    # compare these with https://github.com/AKS1996/jump-gsoc-2020/blob/master/diffcp_sdp_3_py.ipynb
-    # results are not exactly as: 1. there is some residual error   2. diffcp results are SCS specific, hence scaled
-    dx = [-39.6066, 10.8953, -14.9189, 10.9054, 10.883, 10.9118, -21.7508]
-    for (i, vi) in enumerate(x)
-        @test dx[i] ≈ MOI.get(model, DiffOpt.ForwardVariablePrimal(), vi) atol =
-            atol rtol = rtol
+
+    @objective(model, Min, 4x[3] + x[2])
+    return model
+end
+
+function test_differentiating_conic_with_PSD_constraints()
+    model = _build_simple_sdp()
+    optimize!(model)
+    x = model[:x]
+    c1 = model[:c1]
+    c2 = model[:c2]
+    sx = value.(x)
+    @test sx ≈ [2.0, 3.0 - sqrt(2), sqrt(2) - 1] atol = ATOL rtol = RTOL
+
+    for i in 1:3
+        _model = _build_simple_sdp()
+        JuMP.set_normalized_coefficient(_model[:c1], _model[:x][i], 1.001)
+        optimize!(_model)
+        _dx = (value(_model[:x][i]) - value(sx[i])) / 0.001
+        i in (1, 3) ? (@test abs(_dx) < 0.05) : (@test -1.6 < _dx < -1.45)
+        MOI.set(model, DiffOpt.ForwardConstraintFunction(), c1, x[i] + 0.0)
+        DiffOpt.forward_differentiate!(model)
+        _dx = MOI.get(model, DiffOpt.ForwardVariablePrimal(), x[i])
+        i in (1, 3) ? (@test abs(_dx) < 0.05) : (@test -1.6 < _dx < -1.45)
+        MOI.set(model, DiffOpt.ReverseVariablePrimal(), x[i], 1.0)
+        DiffOpt.reverse_differentiate!(model)
+        _dx = JuMP.coefficient(
+            MOI.get(model, DiffOpt.ReverseConstraintFunction(), c1),
+            x[i],
+        )
+        i in (1, 3) ? (@test abs(_dx) < 0.05) : (@test -1.6 < _dx < -1.45)
+        DiffOpt.empty_input_sensitivities!(model)
     end
-    # @test dy ≈ [0.0, -3.56905, 0.0, -0.380035, 0.0, -0.41398, -0.385321, -0.00743119, -0.644986, -0.550542, -2.36765] atol=atol rtol=rtol
-    # @test ds ≈ [0.0, 0.0, -50.4973, 0.0, -25.8066, 0.0, 0.0, 0.0, -7.96528, -1.62968, -2.18925] atol=atol rtol=rtol
-    # TODO: future example, how to differentiate wrt a specific constraint/variable, refer QPLib article for more
-    dA = zeros(11, 7)
-    dA[3:8, 1:6] = Matrix{Float64}(LinearAlgebra.I, 6, 6)  # differentiating only wrt POS constraint c2
-    db = zeros(11)
-    dc = zeros(7)
-    # db = zeros(11)
-    # dA = zeros(11, 7)
-    # dA[3:8, 1:6] = Matrix{Float64}(LinearAlgebra.I, 6, 6)  # differentiating only wrt POS constraint c2
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c1,
-        MOI.Utilities.zero_with_output_dimension(
-            MOI.VectorAffineFunction{Float64},
-            1,
-        ),
-    )
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c2,
-        MOI.Utilities.vectorize(ones(6) .* x[1:6]),
-    )
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c3,
-        MOI.Utilities.zero_with_output_dimension(
-            MOI.VectorAffineFunction{Float64},
-            3,
-        ),
-    )
-    MOI.set(
-        model,
-        DiffOpt.ForwardConstraintFunction(),
-        c4,
-        MOI.Utilities.zero_with_output_dimension(
-            MOI.VectorAffineFunction{Float64},
-            1,
-        ),
-    )
-    DiffOpt.forward_differentiate!(model)
-    # for (i, vi) in enumerate(X)
-    #     @test 0.0 ≈ MOI.get(model,
-    #         DiffOpt.ForwardVariablePrimal(), vi) atol=1e-2 rtol=RTOL
-    # end
-    # TODO add a test here, probably on duals
-    # # note that there's no change in the PSD slack values or dual optimas
-    # @test dy ≈ [0.0, 0.0, 0.0, 0.125978, 0.0, 0.142644, 0.142641, 0.0127401, 0.0, 0.0, 0.0] atol=atol rtol=RTOL
-    # @test ds ≈ [0.0, 0.0, -6.66672, 0.0, -3.33336, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] atol=atol rtol=RTOL
+    for i in 1:3
+        DiffOpt.empty_input_sensitivities!(model)
+        _model = _build_simple_sdp()
+        JuMP.set_normalized_coefficient(_model[:c2][i], _model[:x][i], 1.001)
+        optimize!(_model)
+        _dx = (value(_model[:x][i]) - value(sx[i])) / 0.001
+        @test abs(_dx) < 0.15
+        MOI.set(model, DiffOpt.ForwardConstraintFunction(), c2[i], x[i] + 0.0)
+        DiffOpt.forward_differentiate!(model)
+        _dx = MOI.get(model, DiffOpt.ForwardVariablePrimal(), x[i])
+        @test abs(_dx) < 0.15
+        MOI.set(model, DiffOpt.ReverseVariablePrimal(), x[i], 1.0)
+        DiffOpt.reverse_differentiate!(model)
+        _dx = JuMP.coefficient(
+            MOI.get(model, DiffOpt.ReverseConstraintFunction(), c2[i]),
+            x[i],
+        )
+        @test abs(_dx) < 0.15
+    end
+
     return
 end
 
diff --git a/test/jump.jl b/test/jump.jl
index 8055f1f1..bdb031b7 100644
--- a/test/jump.jl
+++ b/test/jump.jl
@@ -31,6 +31,49 @@ function runtests()
     return
 end
 
+function test_single_variable_objective_forward()
+    model = Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
+    @variable(model, x[1:7] >= 0)
+    @constraint(model, c1, sum(x[i] for i in 1:6) == 10)
+    @constraint(model, c2, x[7] == 10)
+    @constraint(
+        model,
+        c3,
+        LinearAlgebra.Symmetric([
+            x[7] 0.0
+            0.0 x[1]
+        ]) in PSDCone()
+    )
+    @objective(model, Max, x[7])
+    optimize!(model)
+    MOI.set(model, DiffOpt.ForwardObjectiveFunction(), sum(x))
+    DiffOpt.forward_differentiate!(model)
+    @test MOI.get(model, DiffOpt.ForwardVariablePrimal(), x[7]) ≈ 0 atol = ATOL
+    return
+end
+
+function test_single_variable_objective_reverse()
+    model = Model(() -> DiffOpt.diff_optimizer(SCS.Optimizer))
+    @variable(model, x[1:7] >= 0)
+    @constraint(model, c1, sum(x[i] for i in 1:6) == 10)
+    @constraint(model, c2, x[7] == 10)
+    @constraint(
+        model,
+        c3,
+        LinearAlgebra.Symmetric([
+            x[7] 0.0
+            0.0 x[1]
+        ]) in PSDCone()
+    )
+    @objective(model, Max, x[7])
+    optimize!(model)
+    MOI.set(model, DiffOpt.ReverseVariablePrimal(), x[7], 1.0)
+    DiffOpt.reverse_differentiate!(model)
+    func = MOI.get(model, DiffOpt.ReverseObjectiveFunction())
+    @test JuMP.coefficient(func, x[7]) ≈ 0.0 atol = ATOL rtol = RTOL
+    return
+end
+
 function test_forward_on_trivial_qp()
     # using example on https://osqp.org/docs/examples/setup-and-solve.html
     Q = [4.0 1.0; 1.0 2.0]
diff --git a/test/jump_wrapper.jl b/test/jump_wrapper.jl
index dae907c3..1720246e 100644
--- a/test/jump_wrapper.jl
+++ b/test/jump_wrapper.jl
@@ -33,9 +33,9 @@ function test_jump_api()
             (DiffOpt.quadratic_diff_model, HiGHS.Optimizer),
             (DiffOpt.quadratic_diff_model, SCS.Optimizer),
             (DiffOpt.quadratic_diff_model, Ipopt.Optimizer),
-            # (DiffOpt.conic_diff_model, HiGHS.Optimizer),
-            # (DiffOpt.conic_diff_model, SCS.Optimizer), # conicmodel has a issue with sign
-            # (DiffOpt.conic_diff_model, Ipopt.Optimizer),
+            (DiffOpt.conic_diff_model, HiGHS.Optimizer),
+            (DiffOpt.conic_diff_model, SCS.Optimizer),
+            (DiffOpt.conic_diff_model, Ipopt.Optimizer),
             # (DiffOpt.nonlinear_diff_model, HiGHS.Optimizer), #  SQF ctr not supported?
             # (DiffOpt.nonlinear_diff_model, SCS.Optimizer), # returns zero for sensitivity
             (DiffOpt.nonlinear_diff_model, Ipopt.Optimizer),