Support Enzyme.jl

[amontoison]

Just opened for CI, will be included in #311
-> Compute sparse jacobian with Enzyme.

[github-actions]

Package name	latest	stable
ExpressionTreeForge
JSOSuite
PartiallySeparableNLPModels
PartiallySeparableSolvers
SolverTest

[amontoison]

@michel2323

Basic Hessian derivative with backend=ADNLPModels.SparseEnzymeADHessian and T=Float32: Test Failed at /cache/build/tester-amdci4-13/julialang/adnlpmodels-dot-jl/test/sparse_hessian.jl:76
  Expression: H == [x[2] 0; x[1] + x[2] x[1]] + y[2] * [-20 0; 0 0]
   Evaluated: sparse([1, 2, 2], [1, 1, 2], Float32[0.15454096, 0.81299055, 0.6584496], 2, 2) == Float32[-2.5177271 0.0; 0.81299055 0.6584496]

[amontoison]

@michel2323
I have this error with the latest release of Enzyme.jl:

Basic Hessian derivative with backend=ADNLPModels.SparseEnzymeADHessian and T=Float64: Error During Test at /cache/build/tester-amdci4-13/julialang/adnlpmodels-dot-jl/test/sparse_hessian.jl:73
  Test threw exception
  Expression: hess(nlp, x) == T[802 -400 0 0; -400 1002 -400 0; 0 -400 1002 -400; 0 0 -400 200]
  Constant memory is stored (or returned) to a differentiable variable.
  As a result, Enzyme cannot provably ensure correctness and throws this error.
  This might be due to the use of a constant variable as temporary storage for active memory (https://enzyme.mit.edu/julia/stable/faq/#Runtime-Activity).
  If Enzyme should be able to prove this use non-differentable, open an issue!
  To work around this issue, either:
   a) rewrite this variable to not be conditionally active (fastest, but requires a code change), or
   b) set the Enzyme mode to turn on runtime activity (e.g. autodiff(set_runtime_activity(Reverse), ...) ). This will maintain correctness, but may slightly reduce performance.

It is in the sparse Hessian of the Lagrangian.
Do you have an idea of what is the issue?