[General] Test comparaison NLP model

[ocots]

Compare models with https://jso.dev/NLPModelsTest.jl/dev/#consistency.

Note

We can convert a JuMP model to NLPModel.

[amontoison]

@ocots @jbcaillau
I don't know if you have a different ordering for the constraints, the variables, or both.

using OptimalControlProblems
using OptimalControl
using NLPModelsJuMP
using NLPModelsTest
using NLPModels

using LinearAlgebra
using SparseArrays
using Test

check_nlps = false

function jac_and_hess(nlp_oc, nlp_jp)
    jac_oc = jac(nlp_oc, nlp_oc.meta.x0)
    jac_jp = jac(nlp_jp, nlp_jp.meta.x0)
    hess_oc = hess(nlp_oc, nlp_oc.meta.x0).data
    hess_jp = hess(nlp_jp, nlp_jp.meta.x0).data
    return jac_oc, jac_jp, hess_oc, hess_jp
end

docp = beam(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = beam(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = chain(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = chain(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
@test nnz(jac_oc) == nnz(jac_jp)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = double_oscillator(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = double_oscillator(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = ducted_fan(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = ducted_fan(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = electric_vehicle(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = electric_vehicle(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = glider(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = glider(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = insurance(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = insurance(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = jackson(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = jackson(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = robbins(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = robbins(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = robot(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = robot(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = rocket(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = rocket(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = space_shuttle(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = space_shuttle(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = steering(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = steering(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

docp = vanderpol(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = vanderpol(JuMPBackend()) |> MathOptNLPModel
check_nlps && consistent_nlps([nlp_oc, nlp_jp])
jac_oc, jac_jp, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)
@test nnz(jac_oc) == nnz(jac_jp)
@test sort(jac_oc.nzval) ≈ sort(jac_jp.nzval)
# @test nnz(hess_oc) == nnz(hess_jp)

[amontoison]

@jbcaillau @ocots
For the problem ducted_fan, I have a very big difference for the Hessian of the Lagrangian.

docp = ducted_fan(OptimalControlBackend())
nlp_oc = nlp_model(docp)
nlp_jp = ducted_fan(JuMPBackend()) |> MathOptNLPModel
_, _, hess_oc, hess_jp = jac_and_hess(nlp_oc, nlp_jp)

julia> hess_oc
2009×2009 SparseMatrixCSC{Float64, Int64} with 2762 stored entries:
⎡⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤
⎢⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⎥
⎣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣓⣄⎦

julia> hess_jp
2009×2009 SparseMatrixCSC{Float64, Int64} with 129763 stored entries:
⎡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⎥
⎣⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⎦

Do you understand why we have a dense triangle in the right bottom part of the sparse Hessian?

[ocots]

Just to say that ducted_fan is very sensitive and I planned to remove it :-)

I will have a look at all what you wrote @amontoison. Thanks for all the comments.

[amontoison]

@ocots Do you mean numerically sensitive or something else?
Here, it is entirely related to model components and to the sparsity pattern of the subexpressions.
I am mostly curious to understand why the structure of the Hessian of the Lagrangian is so different, since it impacts the sparse linear solvers in the optimization solvers.

[ocots]

@amontoison Sometimes I have this error, sometimes not, depending on the machine or something else:

https://github.com/control-toolbox/OptimalControlProblems.jl/actions/runs/19191504673/job/54866576713#step:8:25

[amontoison]

Wow if x = Inf it means that the problem is nasty enough to get some overflow.
One solution is to scale the model itself.
I will have have a look to the model, I am curious.