diff --git a/.github/workflows/DowngradeSublibraries.yml b/.github/workflows/DowngradeSublibraries.yml
index 33f9c61cc..d9f6216b6 100644
--- a/.github/workflows/DowngradeSublibraries.yml
+++ b/.github/workflows/DowngradeSublibraries.yml
@@ -23,6 +23,81 @@ jobs:
       # ModelingToolkit 11). Stdlibs and in-repo sublibraries are auto-populated by
       # the centralized workflow.
       skip: "SymbolicAnalysis"
+      exclude: "OptimizationQuadDIRECT"
       group-env-name: "OPTIMIZATION_TEST_GROUP"
       group-env-value: "Core"
-      # Every lib/* sublibrary is downgrade-tested (projects auto-discovered, no exclusions).
+      # OptimizationQuadDIRECT has an unregistered URL source and is tested below
+      # with a manifest repair step after downgrade-compat.
+
+  downgrade-quaddirect:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v7
+      - uses: julia-actions/setup-julia@v3
+        with:
+          version: "lts"
+      - name: "Resolve numeric Julia version for downgrade-compat"
+        run: echo "JULIA_MM=$(julia --startup-file=no -e 'print(VERSION.major, ".", VERSION.minor)')" >> "$GITHUB_ENV"
+      - name: "Set sublibrary test group"
+        run: echo "OPTIMIZATION_TEST_GROUP=Core" >> "$GITHUB_ENV"
+      - name: "Enumerate Julia standard libraries"
+        run: |
+          names="$(julia --startup-file=no -e '
+            using Pkg
+            ns = String[]
+            for v in values(Pkg.Types.stdlibs())
+                push!(ns, v isa AbstractString ? v : first(v))
+            end
+            println(join(sort(unique(ns)), ","))
+          ')"
+          echo "STDLIB_SKIP=$names" >> "$GITHUB_ENV"
+      - name: "Compute effective downgrade skip list"
+        run: |
+          sublibs=""
+          for d in lib/*/; do
+            d="${d%/}"
+            [ -f "$d/Project.toml" ] || continue
+            name="$(basename "$d")"
+            if [ -z "$sublibs" ]; then sublibs="$name"; else sublibs="$sublibs,$name"; fi
+          done
+          effective="$STDLIB_SKIP"
+          [ -n "$sublibs" ] && effective="$effective,$sublibs"
+          src_names="$(julia --startup-file=no -e '
+            using TOML
+            src = get(TOML.parsefile(ARGS[1]), "sources", Dict())
+            println(join(collect(keys(src)), ","))
+          ' "lib/OptimizationQuadDIRECT/Project.toml")"
+          [ -n "$src_names" ] && effective="$effective,$src_names"
+          effective="$effective,SymbolicAnalysis"
+          echo "EFFECTIVE_SKIP=$effective" >> "$GITHUB_ENV"
+      - uses: julia-actions/julia-downgrade-compat@v2
+        with:
+          projects: "lib/OptimizationQuadDIRECT"
+          skip: ${{ env.EFFECTIVE_SKIP }}
+          julia_version: ${{ env.JULIA_MM }}
+      - name: "Restore URL-sourced packages"
+        run: |
+          julia --startup-file=no --project=lib/OptimizationQuadDIRECT -e '
+            using Pkg, TOML
+
+            project = TOML.parsefile(joinpath(ARGS[1], "Project.toml"))
+            deps = get(project, "deps", Dict())
+            specs = Pkg.PackageSpec[]
+            for (pkg, src) in get(project, "sources", Dict())
+                src isa AbstractDict || continue
+                haskey(deps, pkg) || continue
+                haskey(src, "url") || continue
+                kwargs = Dict{Symbol, Any}(:name => pkg, :url => src["url"])
+                haskey(src, "rev") && (kwargs[:rev] = src["rev"])
+                haskey(src, "subdir") && (kwargs[:subdir] = src["subdir"])
+                push!(specs, Pkg.PackageSpec(; kwargs...))
+            end
+            isempty(specs) || Pkg.add(specs; preserve = Pkg.PRESERVE_ALL)
+          ' "lib/OptimizationQuadDIRECT"
+      - uses: julia-actions/julia-buildpkg@v1
+        with:
+          project: "lib/OptimizationQuadDIRECT"
+      - uses: julia-actions/julia-runtest@v1
+        with:
+          project: "lib/OptimizationQuadDIRECT"
+          allow_reresolve: false
diff --git a/lib/OptimizationBBO/Project.toml b/lib/OptimizationBBO/Project.toml
index c79d67019..071c15751 100644
--- a/lib/OptimizationBBO/Project.toml
+++ b/lib/OptimizationBBO/Project.toml
@@ -8,6 +8,9 @@ OptimizationBase = "bca83a33-5cc9-4baa-983d-23429ab6bcbb"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 
+[weakdeps]
+LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+
 [extras]
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
@@ -19,6 +22,7 @@ OptimizationBase = {path = "../OptimizationBase"}
 
 [compat]
 BlackBoxOptim = "0.6.3"
+LogExpFunctions = "0.3.28"
 OptimizationBase = "5"
 Pkg = "1"
 Random = "1.10"
diff --git a/lib/OptimizationBase/Project.toml b/lib/OptimizationBase/Project.toml
index bcc673caf..7b966e487 100644
--- a/lib/OptimizationBase/Project.toml
+++ b/lib/OptimizationBase/Project.toml
@@ -48,7 +48,7 @@ OptimizationLBFGSB = {path = "../OptimizationLBFGSB"}
 OptimizationManopt = {path = "../OptimizationManopt"}
 
 [compat]
-ADTypes = "1.14"
+ADTypes = "1.18"
 Aqua = "0.8"
 ArrayInterface = "7.6"
 BenchmarkTools = "1"
diff --git a/lib/OptimizationMOI/Project.toml b/lib/OptimizationMOI/Project.toml
index bd095cc48..18e686850 100644
--- a/lib/OptimizationMOI/Project.toml
+++ b/lib/OptimizationMOI/Project.toml
@@ -33,12 +33,12 @@ Juniper = "0.9"
 LinearAlgebra = "1"
 MathOptInterface = "1.45"
 ModelingToolkit = "11"
-ModelingToolkitBase = "1"
+ModelingToolkitBase = "1.17"
 NLopt = "1"
 OptimizationBase = "5.1"
-Reexport = "1.2"
+Reexport = "1.2.2"
 ReverseDiff = "1"
-SciMLBase = "2.130, 3"
+SciMLBase = "2.146, 3"
 SciMLStructures = "1"
 SparseArrays = "1.6"
 SymbolicIndexingInterface = "0.3.46"
diff --git a/lib/OptimizationMadNLP/Project.toml b/lib/OptimizationMadNLP/Project.toml
index 24b218329..ba331d8d2 100644
--- a/lib/OptimizationMadNLP/Project.toml
+++ b/lib/OptimizationMadNLP/Project.toml
@@ -26,10 +26,10 @@ OptimizationBase = "5.1"
 OptimizationNLPModels = "1.3"
 Pkg = "1"
 Random = "1.10"
-Reexport = "1.2"
+Reexport = "1.2.2"
 ReverseDiff = "1"
 SafeTestsets = "0.1"
-SciMLBase = "2.130, 3"
+SciMLBase = "2.146, 3"
 SparseArrays = "1.10"
 SymbolicIndexingInterface = "0.3.46"
 Symbolics = "7"
diff --git a/lib/OptimizationMadNLP/test/core_tests.jl b/lib/OptimizationMadNLP/test/core_tests.jl
index d3a2ae401..6fc7513c2 100644
--- a/lib/OptimizationMadNLP/test/core_tests.jl
+++ b/lib/OptimizationMadNLP/test/core_tests.jl
@@ -364,16 +364,18 @@ end
                 MadNLP.CompactLBFGS,
                 MadNLP.ExactHessian,  # For comparison
             ]
+            initial_u = variant == MadNLP.ExactHessian ? x0[1:2] : x0
             # Only provide gradients, no Hessian needed for LBFGS
             ad = AutoForwardDiff()  # First-order AD is sufficient
             optfunc = OptimizationFunction(extended_rosenbrock, ad)
-            prob = OptimizationProblem(optfunc, x0, nothing)
+            prob = OptimizationProblem(optfunc, initial_u, nothing)
 
             if variant == MadNLP.ExactHessian
+                # Exact Hessian is only a comparison here; the LBFGS path keeps the larger problem.
                 # Use second-order AD for exact Hessian
                 ad = SecondOrder(AutoForwardDiff(), AutoForwardDiff())
                 optfunc = OptimizationFunction(extended_rosenbrock, ad)
-                prob = OptimizationProblem(optfunc, x0, nothing)
+                prob = OptimizationProblem(optfunc, initial_u, nothing)
             end
 
             opt = MadNLPOptimizer(
@@ -458,8 +460,8 @@ end
             return x0
         end
 
-        @testset "N=5 electrons with $approx" for approx in [MadNLP.CompactLBFGS, MadNLP.ExactHessian]
-            np = 5
+        @testset "electrons on sphere with $approx" for approx in [MadNLP.CompactLBFGS, MadNLP.ExactHessian]
+            np = approx == MadNLP.ExactHessian ? 2 : 5
             x0 = init_electrons_on_sphere(np)
 
             if approx == MadNLP.CompactLBFGS
@@ -499,10 +501,9 @@ end
             unit_sphere_constraints(cons_vals, sol.u, nothing)
             @test all(abs.(cons_vals) .< 1.0e-5)
 
-            # Known optimal energy for 5 electrons on unit sphere
+            # Known optimal energy for electrons on unit sphere
             # Reference: https://en.wikipedia.org/wiki/Thomson_problem
-            # Configuration: Triangular dipyramid (trigonal bipyramid, D3h symmetry)
-            expected_energy = 6.474691495
+            expected_energy = np == 2 ? 0.5 : 6.474691495
             @test isapprox(sol.objective, expected_energy, rtol = 1.0e-3)
 
             # Verify minimum distance between electrons
@@ -520,17 +521,14 @@ end
             @test min_dist > 0.5  # Electrons should be well-separated
         end
 
-        @testset verbose = true "LBFGS vs Exact Hessian" begin
-            # Test with moderate size to show LBFGS efficiency
-            np = 10  # Gyroelongated square dipyramid configuration
-            x0 = init_electrons_on_sphere(np)
-
+        @testset verbose = true "LBFGS and Exact Hessian" begin
             results = []
 
-            for (name, approx, ad) in [
+            for (name, approx, ad, np, expected_energy) in [
                     (
                         "CompactLBFGS", MadNLP.CompactLBFGS,
-                        AutoForwardDiff(),
+                        AutoForwardDiff(), 10,
+                        32.71694946,
                     )
                     (
                         "ExactHessian",
@@ -538,8 +536,11 @@ end
                         SecondOrder(
                             AutoForwardDiff(), AutoZygote()
                         ),
+                        2,
+                        0.5,
                     )
                 ]
+                x0 = init_electrons_on_sphere(np)
                 optfunc = OptimizationFunction(
                     coulomb_potential, ad,
                     cons = unit_sphere_constraints
@@ -562,6 +563,7 @@ end
                         objective = sol.objective,
                         iterations = sol.stats.iterations,
                         success = SciMLBase.successful_retcode(sol),
+                        expected = expected_energy,
                     )
                 )
             end
@@ -569,11 +571,10 @@ end
             # All methods should converge
             @test all(r[2].success for r in values(results))
 
-            # All should find similar objective values (gyroelongated square dipyramid energy)
+            # Check objective values against the corresponding Thomson problem energy.
             # Reference: https://en.wikipedia.org/wiki/Thomson_problem
-            objectives = [r[2].objective for r in values(results)]
-            @testset "$(results[i][1])" for (i, o) in enumerate(objectives)
-                @test o ≈ 32.71694946 rtol = 1.0e-2
+            @testset "$(name)" for (name, result) in results
+                @test result.objective ≈ result.expected rtol = 1.0e-2
             end
 
             # LBFGS methods typically need more iterations but less cost per iteration
diff --git a/lib/OptimizationNLPModels/Project.toml b/lib/OptimizationNLPModels/Project.toml
index 78433dfd4..37075fb0e 100644
--- a/lib/OptimizationNLPModels/Project.toml
+++ b/lib/OptimizationNLPModels/Project.toml
@@ -27,10 +27,10 @@ OptimizationLBFGSB = "1.2"
 OptimizationMOI = "1"
 OptimizationOptimJL = "0.4.10"
 Pkg = "1"
-Reexport = "1.2"
+Reexport = "1.2.2"
 ReverseDiff = "1"
 SafeTestsets = "0.1"
-SciMLBase = "2.130, 3"
+SciMLBase = "2.146, 3"
 SparseArrays = "1.10.0"
 Test = "1.10"
 Zygote = "0.6, 0.7"
diff --git a/lib/OptimizationNOMAD/Project.toml b/lib/OptimizationNOMAD/Project.toml
index 8e705e4c4..793d248d3 100644
--- a/lib/OptimizationNOMAD/Project.toml
+++ b/lib/OptimizationNOMAD/Project.toml
@@ -8,6 +8,9 @@ NOMAD = "02130f1c-4665-5b79-af82-ff1385104aa0"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 
+[weakdeps]
+LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+
 [extras]
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
@@ -18,6 +21,7 @@ OptimizationBase = {path = "../OptimizationBase"}
 
 [compat]
 Pkg = "1"
+LogExpFunctions = "0.3.28"
 SafeTestsets = "0.1"
 julia = "1.10"
 OptimizationBase = "5"
diff --git a/lib/OptimizationSciPy/Project.toml b/lib/OptimizationSciPy/Project.toml
index 87566f549..bccc4cfdf 100644
--- a/lib/OptimizationSciPy/Project.toml
+++ b/lib/OptimizationSciPy/Project.toml
@@ -23,7 +23,7 @@ ForwardDiff = "0.10, 1"
 ModelingToolkit = "11"
 OptimizationBase = "5.1"
 Pkg = "1"
-PythonCall = "0.9.24"
+PythonCall = "0.9.30"
 Random = "1.10"
 Reexport = "1.2"
 ReverseDiff = "1"
diff --git a/lib/SimpleOptimization/Project.toml b/lib/SimpleOptimization/Project.toml
index ec6b254f7..6dbb09b9f 100644
--- a/lib/SimpleOptimization/Project.toml
+++ b/lib/SimpleOptimization/Project.toml
@@ -6,6 +6,7 @@ authors = ["Utkarsh <rajpututkarsh530@gmail.com> and contributors"]
 [weakdeps]
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 
 [deps]
 OptimizationBase = "bca83a33-5cc9-4baa-983d-23429ab6bcbb"
@@ -29,7 +30,8 @@ SimpleOptimizationEnzymeExt = "Enzyme"
 SimpleOptimizationForwardDiffExt = "ForwardDiff"
 
 [compat]
-ADTypes = "1.14"
+ADTypes = "1.18"
+DifferentiationInterface = "0.7.13"
 Enzyme = "0.13"
 ForwardDiff = "0.10, 1"
 LinearAlgebra = "1.10"
@@ -38,7 +40,7 @@ Pkg = "1"
 Reexport = "1.2"
 SafeTestsets = "0.1"
 SciMLBase = "2.122.1, 3"
-SimpleNonlinearSolve = "1, 2"
+SimpleNonlinearSolve = "2.12"
 Test = "1.10"
 julia = "1.10"