Recognize sparse explicit second-order AD

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: ChrisRackauckas

lib/OptimizationBase/src/cache.jl

@@ -74,6 +74,7 @@ function OptimizationCache(
 
     if !(
             prob.f.adtype isa DifferentiationInterface.SecondOrder ||
+                prob.f.adtype isa AutoSparse{<:DifferentiationInterface.SecondOrder} ||
                 prob.f.adtype isa AutoZygote
         ) &&
             (

lib/OptimizationBase/test/core_tests.jl

@@ -5,5 +5,6 @@ using Test
     include("matrixvalued.jl")
     include("solver_missing_error_messages.jl")
     include("lag_h_sigma_zero_test.jl")
+    include("second_order_warning_test.jl")
     include("solve_internals_test.jl")
 end

lib/OptimizationBase/test/second_order_warning_test.jl

@@ -0,0 +1,23 @@
+using DifferentiationInterface: SecondOrder
+using ForwardDiff
+
+struct ExactHessianOptimizer end
+
+SciMLBase.requireshessian(::ExactHessianOptimizer) = true
+
+@testset "explicit sparse second-order AD" begin
+    objective(x, p) = sum(abs2, x)
+    sparse_second_order = AutoSparse(
+        SecondOrder(AutoForwardDiff(), AutoForwardDiff())
+    )
+    explicit_f = OptimizationFunction(objective, sparse_second_order)
+    explicit_prob = OptimizationProblem(explicit_f, [1.0, 1.0])
+
+    @test_nowarn OptimizationCache(explicit_prob, ExactHessianOptimizer())
+
+    implicit_f = OptimizationFunction(objective, AutoSparse(AutoForwardDiff()))
+    implicit_prob = OptimizationProblem(implicit_f, [1.0, 1.0])
+    @test_logs (:warn, r"missing_second_order_ad") match_mode = :any OptimizationCache(
+        implicit_prob, ExactHessianOptimizer()
+    )
+end