[documentation] Explain how we can provide a sparsity pattern

[amontoison]

@tmigot It seems that we can't create an ADNLPModel / ADNLSModel with an initialized AD backend.
I wanted to create nlp with the following constructor:

nlp = ADNLPModel!(f, x0, lvar, uvar, c!, lcon, ucon, acobian_backend=J_backend,hessian_backend=H_backend)

but the code here wants to call the constructor of an ADNLPModels.ADBackend.
We can use set_adbackend! as a workaround.

Related to #284 and control-toolbox/CTDirect.jl#183
cc @jbcaillau

[github-actions]

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
DerivativeFreeSolvers.jl
JSOSolvers.jl
NLPModelsIpopt.jl
OptimalControl.jl
OptimizationProblems.jl
Percival.jl
QuadraticModels.jl
SolverBenchmark.jl
SolverTools.jl

[tmigot]

You could adapt this line

ADNLPModels.jl/src/ad.jl

Line 87 in c13dbf6

hessian_backend = if hessian_backend isa AbstractNLPModel

(and the others) to make it work.

Essentially, we expect 3 types as a jacobian_backend:

• A ADBackend type, and then in the constructor of ADModelBackend we call its constructor;
• An AbstractNLPModel
• An instantiated ADBackend (this is what you want, and is missing right now).

[amontoison]

You could adapt this line

ADNLPModels.jl/src/ad.jl

Line 87 in c13dbf6

hessian_backend = if hessian_backend isa AbstractNLPModel

(and the others) to make it work.
Essentially, we expect 3 types as a jacobian_backend:

• A ADBackend type, and then in the constructor of ADModelBackend we call its constructor;
• An AbstractNLPModel
• An instantiated ADBackend (this is what you want, and is missing right now).

The issue is what can we do to do the difference between an ADBackend type and an insantiated ADBackend?