OptimizationProblems.jl tutorial

by Tangi Migot

In this tutorial, we will see how to access the problems in JuMP and ADNLPModel syntax. This package is subdivided in two submodules: PureJuMP for the JuMP problems, ADNLPProblems for the ADNLPModel problems.

Problems in JuMP syntax: PureJuMP

You can obtain the list of problems currently defined with OptimizationProblems.meta[!, :name].

using OptimizationProblems, OptimizationProblems.PureJuMP
problems = OptimizationProblems.meta[!, :name]
length(problems)
261

Then, it suffices to select any of this problem to get the JuMP model.

jump_model = OptimizationProblems.PureJuMP.zangwil3()
A JuMP Model
Minimization problem with:
Variables: 3
Objective function type: Nonlinear
`JuMP.AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 3 constraints
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
Names registered in the model: constr1, constr2, constr3, x

Note that certain problems are scalable, i.e., their size depends on parameters that can be modified. The list of those problems is available once again using meta:

var_problems = OptimizationProblems.meta[OptimizationProblems.meta.variable_nvar, :name]
length(var_problems)
84

Then, using the keyword n, it is possible to specify the targeted number of variables.

jump_model_12 = OptimizationProblems.PureJuMP.woods(n=12)
A JuMP Model
Minimization problem with:
Variables: 12
Objective function type: Nonlinear
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
Names registered in the model: x
jump_model_120 = OptimizationProblems.PureJuMP.woods(n=120)
A JuMP Model
Minimization problem with:
Variables: 120
Objective function type: Nonlinear
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
Names registered in the model: x

These problems can be converted as NLPModels via NLPModelsJuMP to facilitate evaluating objective, constraints and their derivatives.

using NLPModels, NLPModelsJuMP
nlp_model_120 = MathOptNLPModel(jump_model_120)
obj(nlp_model_120, zeros(120))
Error: ArgumentError: Package NLPModelsJuMP not found in current path:
- Run `import Pkg; Pkg.add("NLPModelsJuMP")` to install the NLPModelsJuMP p
ackage.

Problems in ADNLPModel syntax: ADNLPProblems

This package also offers ADNLPModel test problems. This is an optional dependency, so ADNLPModels has to be added first.

using ADNLPModels

You can obtain the list of problems currently defined with OptimizationProblems.meta[!, :name]:

using OptimizationProblems, OptimizationProblems.ADNLPProblems
problems = OptimizationProblems.meta[!, :name]
length(problems)
261

Similarly, to the PureJuMP models, it suffices to select any of this problem to get the model.

nlp = OptimizationProblems.ADNLPProblems.zangwil3()
ADNLPModel - Model with automatic differentiation backend ADNLPModels.ADMod
elBackend{ADNLPModels.ForwardDiffADGradient, ADNLPModels.ForwardDiffADHvpro
d, ADNLPModels.ForwardDiffADJprod, ADNLPModels.ForwardDiffADJtprod, ADNLPMo
dels.ForwardDiffADJacobian, ADNLPModels.ForwardDiffADHessian, ADNLPModels.F
orwardDiffADGHjvprod}(ADNLPModels.ForwardDiffADGradient(ForwardDiff.Gradien
tConfig{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1332"{Flo
at64}, Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optimi
zationProblems.ADNLPProblems.var"#f#1332"{Float64}, Float64}, Float64, 3}}}
((Partials(1.0, 0.0, 0.0), Partials(0.0, 1.0, 0.0), Partials(0.0, 0.0, 1.0)
), ForwardDiff.Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"
#f#1332"{Float64}, Float64}, Float64, 3}[Dual{ForwardDiff.Tag{OptimizationP
roblems.ADNLPProblems.var"#f#1332"{Float64}, Float64}}(0.0,0.0,0.0,0.0), Du
al{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1332"{Float64}
, Float64}}(0.0,0.0,0.0,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.ADN
LPProblems.var"#f#1332"{Float64}, Float64}}(0.0,0.0,0.0,0.0)])), ADNLPModel
s.ForwardDiffADHvprod(), ADNLPModels.ForwardDiffADJprod(), ADNLPModels.Forw
ardDiffADJtprod(), ADNLPModels.ForwardDiffADJacobian(9), ADNLPModels.Forwar
dDiffADHessian(6), ADNLPModels.ForwardDiffADGHjvprod())
  Problem name: zangwil3
   All variables: ████████████████████ 3      All constraints: ████████████
████████ 3     
            free: ████████████████████ 3                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████
████████ 3     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   6               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ████████████
████████ 3     
                                                         nnzj: (  0.00% spa
rsity)   9     

  Counters:
             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0

Note that some of these problems are scalable, i.e., their size depends on some parameters that can be modified.

nlp_12 = OptimizationProblems.ADNLPProblems.woods(n=12)
ADNLPModel - Model with automatic differentiation backend ADNLPModels.ADMod
elBackend{ADNLPModels.ForwardDiffADGradient, ADNLPModels.ForwardDiffADHvpro
d, ADNLPModels.ForwardDiffADJprod, ADNLPModels.ForwardDiffADJtprod, ADNLPMo
dels.ForwardDiffADJacobian, ADNLPModels.ForwardDiffADHessian, ADNLPModels.F
orwardDiffADGHjvprod}(ADNLPModels.ForwardDiffADGradient(ForwardDiff.Gradien
tConfig{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Flo
at64}, Float64}, Float64, 12, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optim
izationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}, Float64, 12}
}}((Partials(1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), P
artials(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partia
ls(0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0)), ForwardDiff.Dual{ForwardDiff.Tag{OptimizationProblems.A
DNLPProblems.var"#f#1329"{Float64}, Float64}, Float64, 12}[Dual{ForwardDiff
.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(2.
1219957915e-314,3.8195924245e-313,2.5463949502e-313,5.304989478e-313,6.5781
869534e-313,4.6683907412e-313,4.6683907412e-313,4.66839074175e-313,2.546394
9509e-313,8.912382324e-313,7.6391848497e-313,7.63918484925e-313,9.973380219
3e-313), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#132
9"{Float64}, Float64}}(1.06099789566e-312,2.5463949517e-313,2.33419537065e-
313,2.3341953706e-313,2.3341953706e-313,2.3341953706e-313,4.243991582e-314,
1.10343781131e-312,4.2439916076e-314,1.12465776922e-312,4.243991608e-314,1.
14587772713e-312,4.2439916086e-314), Dual{ForwardDiff.Tag{OptimizationProbl
ems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(1.16709768504e-312,4.243
991609e-314,1.18831764295e-312,4.2439916096e-314,1.20953760086e-312,4.24399
161e-314,6.9033212082815e-310,6.90332120828465e-310,6.9033212082878e-310,6.
903321208291e-310,6.90332120829414e-310,6.9033212082973e-310,6.903321208300
46e-310), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#13
29"{Float64}, Float64}}(6.90332120830363e-310,6.9033212083068e-310,6.903321
20830995e-310,6.9033212083131e-310,6.90332120831627e-310,6.90332120831944e-
310,6.9033212083226e-310,6.90332120832576e-310,6.9033212083289e-310,6.90332
12083321e-310,6.90332120833525e-310,6.9033212083384e-310,6.90332120834157e-
310), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{
Float64}, Float64}}(6.90332120834473e-310,6.9033212083479e-310,6.9033212083
5106e-310,6.9033212083542e-310,6.9033212083574e-310,6.90332120836054e-310,6
.9033212083637e-310,6.90332120836687e-310,6.90332120837003e-310,6.903321208
17517e-310,6.9033212083732e-310,6.90332120817517e-310,6.90332120837635e-310
), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Flo
at64}, Float64}}(6.90332120838584e-310,6.90332120817517e-310,6.903321208205
6e-310,6.903321208389e-310,6.90332120839216e-310,6.90332120817517e-310,6.90
33212083795e-310,6.90332120817517e-310,6.9033212083795e-310,6.9033212081751
7e-310,6.9033212083827e-310,6.90332120817517e-310,6.9033212083827e-310), Du
al{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}
, Float64}}(6.90332120817517e-310,6.9033212082056e-310,6.9033212083953e-310
,6.90332120817517e-310,6.90332120840165e-310,6.9033212084048e-310,6.9033212
0840797e-310,6.90332120841113e-310,6.9033212084143e-310,6.90332120841746e-3
10,6.9033212084206e-310,6.9033212084238e-310,6.90332120842694e-310), Dual{F
orwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Fl
oat64}}(6.9033212084301e-310,6.90332120843327e-310,6.90332120843643e-310,6.
9033212084396e-310,6.90332120844275e-310,6.9033212084459e-310,6.90332120844
91e-310,6.90332120845224e-310,6.9033212084554e-310,6.90332120845856e-310,6.
90332120846173e-310,6.9033212084649e-310,6.90332120846805e-310), Dual{Forwa
rdDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float6
4}}(6.9033212084712e-310,6.90332120847437e-310,6.90332120847754e-310,6.9033
212084807e-310,6.90332120848386e-310,6.903321208487e-310,6.9033212084902e-3
10,6.90332120849335e-310,6.9033212084965e-310,6.90332120849967e-310,6.90332
120850283e-310,6.903321208506e-310,6.90332120850916e-310), Dual{ForwardDiff
.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.
9033212085123e-310,6.9033212085155e-310,6.90332120851864e-310,6.90332120852
18e-310,6.90332120852497e-310,6.90332120852813e-310,6.9033212085313e-310,6.
90332120853445e-310,6.9033212085376e-310,6.9033212085408e-310,6.90332120854
394e-310,6.9033212085471e-310,6.90332120855026e-310), Dual{ForwardDiff.Tag{
OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.90332
120855342e-310,6.9033212085566e-310,6.90332120855975e-310,6.9033212085629e-
310,6.90332120856607e-310,6.90332120856924e-310,6.9033212085724e-310,6.9033
2120857556e-310,6.9033212085787e-310,6.9033212085819e-310,6.90332120858505e
-310,6.9033212085882e-310,6.90332120859137e-310), Dual{ForwardDiff.Tag{Opti
mizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.903321208
59453e-310,6.9033212085977e-310,6.90332120860086e-310,6.903321208604e-310,6
.9033212086072e-310,6.90332120861034e-310,6.9033212086135e-310,6.9033212086
1667e-310,6.90332120837635e-310,6.9033212083795e-310,6.9033212083827e-310,0
.0,0.0)])), ADNLPModels.ForwardDiffADHvprod(), ADNLPModels.ForwardDiffADJpr
od(), ADNLPModels.ForwardDiffADJtprod(), ADNLPModels.ForwardDiffADJacobian(
0), ADNLPModels.ForwardDiffADHessian(78), ADNLPModels.ForwardDiffADGHjvprod
())
  Problem name: woods
   All variables: ████████████████████ 12     All constraints: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            free: ████████████████████ 12                free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   78              linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                         nnzj: (------% spa
rsity)         

  Counters:
             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0
nlp_120 = OptimizationProblems.ADNLPProblems.woods(n=120)
ADNLPModel - Model with automatic differentiation backend ADNLPModels.ADMod
elBackend{ADNLPModels.ForwardDiffADGradient, ADNLPModels.ForwardDiffADHvpro
d, ADNLPModels.ForwardDiffADJprod, ADNLPModels.ForwardDiffADJtprod, ADNLPMo
dels.ForwardDiffADJacobian, ADNLPModels.ForwardDiffADHessian, ADNLPModels.F
orwardDiffADGHjvprod}(ADNLPModels.ForwardDiffADGradient(ForwardDiff.Gradien
tConfig{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Flo
at64}, Float64}, Float64, 12, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optim
izationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}, Float64, 12}
}}((Partials(1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), P
artials(0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partia
ls(0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0, 0.0), Partials(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.
0, 0.0, 0.0, 1.0)), ForwardDiff.Dual{ForwardDiff.Tag{OptimizationProblems.A
DNLPProblems.var"#f#1329"{Float64}, Float64}, Float64, 12}[Dual{ForwardDiff
.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(0.
0,6.3966703e-316,6.903326239131e-310,3.8341764e-316,6.3966794e-316,6.544963
5e-316,3.56856976e-316,6.39668056e-316,6.903326239131e-310,3.83357165e-316,
0.0,6.59488626e-316,3.56856976e-316), Dual{ForwardDiff.Tag{OptimizationProb
lems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(5.56596175e-316,6.90332
6239131e-310,3.8341835e-316,0.0,1.5965996e-316,3.56856976e-316,5.51260977e-
316,6.903326239131e-310,1.0e-323,0.0,NaN,0.0,2.22944316e-316), Dual{Forward
Diff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}
}(6.903326239131e-310,3.833574e-316,5.48824127e-316,7.5700181e-316,3.568569
76e-316,5.48824246e-316,6.903326239131e-310,3.8341906e-316,5.5125572e-316,5
.48627687e-316,3.56856976e-316,5.5125584e-316,6.903326239131e-310), Dual{Fo
rwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Flo
at64}}(3.8335835e-316,0.0,1.7526548e-316,3.56856976e-316,6.44386265e-316,6.
903326239131e-310,3.8335859e-316,0.0,2.7745794e-316,3.56856976e-316,5.56610
09e-316,6.903326239131e-310,3.8335906e-316), Dual{ForwardDiff.Tag{Optimizat
ionProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.75645956e-316,
6.5948926e-316,3.56856976e-316,6.75646075e-316,6.903326239131e-310,3.834197
73e-316,0.0,3.651738e-316,3.56856976e-316,3.58475535e-316,6.903326239131e-3
10,1.0e-323,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.v
ar"#f#1329"{Float64}, Float64}}(NaN,0.0,0.0,6.903326239131e-310,3.83359774e
-316,4.08117e-316,9.8787497e-316,3.56856976e-316,4.08117117e-316,6.90332623
9131e-310,3.8336001e-316,0.0,1.7526524e-316), Dual{ForwardDiff.Tag{Optimiza
tionProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.56856976e-316
,6.4438516e-316,6.903326239131e-310,3.8336025e-316,0.0,7.3544517e-316,3.568
56976e-316,9.851099e-316,6.903326239131e-310,3.83421196e-316,0.0,1.7286369e
-316,3.56856976e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProbl
ems.var"#f#1329"{Float64}, Float64}}(5.51255365e-316,6.903326239131e-310,1.
0e-323,0.0,NaN,0.0,0.0,6.903326239131e-310,3.8342167e-316,0.0,2.1585222e-31
6,3.56856976e-316,9.85106345e-316), Dual{ForwardDiff.Tag{OptimizationProble
ms.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.903326239131e-310,3.833
61196e-316,4.0810759e-316,2.8514386e-316,3.56856976e-316,4.0810771e-316,6.9
03326239131e-310,3.83476215e-316,6.75640423e-316,4.5738906e-316,3.56856976e
-316,6.7564054e-316,6.903326239131e-310), Dual{ForwardDiff.Tag{Optimization
Problems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.8336167e-316,5.51
256195e-316,9.8787434e-316,3.56856976e-316,5.51256313e-316,6.903326239131e-
310,6.95258723262955e-310,2.81605363e-316,NaN,0.0,2.8160548e-316,6.90332623
9131e-310,6.95258723262955e-310), Dual{ForwardDiff.Tag{OptimizationProblems
.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(0.0,NaN,0.0,5.5661317e-316,
6.903326239131e-310,3.8336238e-316,6.15938637e-316,4.3438307e-316,3.5685697
6e-316,6.15938755e-316,6.903326239131e-310,3.8342096e-316,0.0), Dual{Forwar
dDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64
}}(3.6517467e-316,3.56856976e-316,6.5450987e-316,6.903326239131e-310,3.8342
3567e-316,9.8510528e-316,2.15852854e-316,3.56856976e-316,9.85105397e-316,6.
903326239131e-310,3.83423804e-316,5.48821677e-316,9.3019933e-316), Dual{For
wardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Floa
t64}}(3.56856976e-316,5.48821795e-316,6.903326239131e-310,6.95258723262955e
-310,0.0,NaN,0.0,2.8160493e-316,6.903326239131e-310,3.8342428e-316,3.584794
5e-316,3.42862665e-316,3.56856976e-316), Dual{ForwardDiff.Tag{OptimizationP
roblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.58479566e-316,6.90
3326239131e-310,3.8336357e-316,0.0,4.34382516e-316,3.56856976e-316,6.159392
3e-316,6.903326239131e-310,3.8336404e-316,0.0,2.8514742e-316,3.56856976e-31
6,3.1465784e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.
var"#f#1329"{Float64}, Float64}}(6.903326239131e-310,3.8336428e-316,3.58462
294e-316,3.95147656e-316,3.56856976e-316,3.5846241e-316,6.903326239131e-310
,3.83424516e-316,2.8161572e-316,3.1277948e-316,3.56856976e-316,2.81615837e-
316,6.903326239131e-310), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPPr
oblems.var"#f#1329"{Float64}, Float64}}(3.83364754e-316,5.5126726e-316,5.19
40497e-316,3.56856976e-316,5.5126738e-316,6.903326239131e-310,3.83425465e-3
16,0.0,6.26255953e-316,3.56856976e-316,3.5847498e-316,6.903326239131e-310,3
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"#f#1329"{Float64}, Float64}}(0.0,7.47521006e-316,3.56856976e-316,6.4438587
e-316,6.903326239131e-310,3.834257e-316,0.0,3.1077389e-316,3.56856976e-316,
7.9498791e-316,6.903326239131e-310,3.833657e-316,9.8511421e-316), Dual{Forw
ardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float
64}}(3.1367789e-316,3.56856976e-316,9.8511433e-316,6.903326239131e-310,3.83
36594e-316,3.146544e-316,5.1940552e-316,3.56856976e-316,3.1465452e-316,6.90
3326239131e-310,3.83426887e-316,0.0,3.2063461e-316), Dual{ForwardDiff.Tag{O
ptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.568569
76e-316,5.51271096e-316,6.903326239131e-310,3.83366177e-316,3.1465725e-316,
2.8514797e-316,3.56856976e-316,3.14657367e-316,6.903326239131e-310,3.834273
6e-316,3.58473677e-316,6.26256585e-316,3.56856976e-316), Dual{ForwardDiff.T
ag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.58
473796e-316,6.903326239131e-310,3.8336689e-316,9.85119744e-316,3.13678563e-
316,3.56856976e-316,9.85119863e-316,6.903326239131e-310,3.83427836e-316,9.8
511089e-316,7.35462603e-316,3.56856976e-316,9.8511101e-316), Dual{ForwardDi
ff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(
6.903326239131e-310,3.83428073e-316,0.0,5.1942564e-316,3.56856976e-316,5.51
267855e-316,6.903326239131e-310,3.83427125e-316,6.15933973e-316,4.4935713e-
316,3.56856976e-316,6.1593409e-316,6.903326239131e-310), Dual{ForwardDiff.T
ag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.83
428548e-316,6.1593603e-316,4.49357685e-316,3.56856976e-316,6.15936147e-316,
6.903326239131e-310,6.95258723262955e-310,6.15929467e-316,NaN,0.0,6.1592958
6e-316,6.903326239131e-310,3.8336831e-316), Dual{ForwardDiff.Tag{Optimizati
onProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(0.0,1.7284013e-31
6,3.56856976e-316,5.5127141e-316,6.903326239131e-310,3.8336855e-316,5.51258
487e-316,3.9514655e-316,3.56856976e-316,5.51258606e-316,6.903326239131e-310
,3.83368785e-316,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProbl
ems.var"#f#1329"{Float64}, Float64}}(7.85954175e-316,3.56856976e-316,5.4883
0807e-316,6.903326239131e-310,3.83429496e-316,6.15935e-316,3.2063548e-316,3
.56856976e-316,6.1593512e-316,6.903326239131e-310,3.8342997e-316,0.0,6.2625
5083e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#
1329"{Float64}, Float64}}(3.56856976e-316,3.58475535e-316,6.903326239131e-3
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326239131e-310,3.83369734e-316,0.0,6.59487757e-316,3.56856976e-316), Dual{F
orwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Fl
oat64}}(3.58475535e-316,6.903326239131e-310,3.8342831e-316,2.81604335e-316,
7.4290011e-316,3.56856976e-316,2.81604454e-316,6.903326239131e-310,6.952587
23265248e-310,6.75639474e-316,NaN,0.0,6.75639593e-316), Dual{ForwardDiff.Ta
g{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.903
326239131e-310,3.83431156e-316,0.0,6.5946839e-316,3.56856976e-316,5.5660123
4e-316,6.903326239131e-310,3.83366414e-316,5.56603645e-316,5.56750403e-316,
3.56856976e-316,5.56603764e-316,6.903326239131e-310), Dual{ForwardDiff.Tag{
OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.83370
92e-316,3.58475416e-316,3.2061651e-316,3.56856976e-316,3.58475535e-316,6.90
3326239131e-310,3.833676e-316,5.5660894e-316,6.5184634e-316,3.56856976e-316
,5.5660906e-316,6.903326239131e-310,3.83432105e-316), Dual{ForwardDiff.Tag{
OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(5.51259
83e-316,3.75572854e-316,3.56856976e-316,5.5125995e-316,6.903326239131e-310,
3.8343234e-316,0.0,2.8516046e-316,3.56856976e-316,4.0810866e-316,6.90332623
9131e-310,3.8337187e-316,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.AD
NLPProblems.var"#f#1329"{Float64}, Float64}}(2.2411031e-316,3.56856976e-316
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814e-316,3.56856976e-316,3.14661556e-316,6.903326239131e-310,3.83372343e-31
6,0.0,4.34376113e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProb
lems.var"#f#1329"{Float64}, Float64}}(3.56856976e-316,3.1465523e-316,6.9033
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6,7.949804e-316,6.903326239131e-310,3.8343353e-316,7.94980754e-316,3.691898
4e-316,3.56856976e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPPro
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316,6.903326239131e-310,3.83434e-316,5.5125896e-316,3.75570997e-316,3.56856
976e-316,5.5125908e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPPr
oblems.var"#f#1329"{Float64}, Float64}}(6.903326239131e-310,3.834276e-316,5
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326239131e-310), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.va
r"#f#1329"{Float64}, Float64}}(3.8337258e-316,0.0,2.15869533e-316,3.5685697
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{Float64}, Float64}}(0.0,3.7557155e-316,3.56856976e-316,5.51259476e-316,6.9
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329"{Float64}, Float64}}(0.0,4.08114745e-316,6.903326239131e-310,3.8337851e
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16,6.3966343e-316,4.847748e-316,3.56856976e-316,6.3966355e-316,6.9033262391
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timizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(0.0,6.518
3725e-316,3.56856976e-316,3.14653967e-316,6.903326239131e-310,3.8346934e-31
6,0.0,3.95145245e-316,3.56856976e-316,5.5125813e-316,6.903326239131e-310,3.
83408627e-316,5.51268606e-316), Dual{ForwardDiff.Tag{OptimizationProblems.A
DNLPProblems.var"#f#1329"{Float64}, Float64}}(5.5552425e-316,3.56856976e-31
6,5.51268724e-316,6.903326239131e-310,1.0e-323,0.0,NaN,0.0,2.22949297e-316,
6.903326239131e-310,1.0e-323,0.0,NaN), Dual{ForwardDiff.Tag{OptimizationPro
blems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(0.0,0.0,6.903326239131
e-310,3.83409575e-316,0.0,5.47480703e-316,3.56856976e-316,5.4882472e-316,6.
903326239131e-310,3.8346815e-316,0.0,6.5947179e-316,3.56856976e-316), Dual{
ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, F
loat64}}(5.5660811e-316,6.903326239131e-310,1.0e-323,0.0,NaN,0.0,2.22949297
e-316,6.903326239131e-310,3.83410287e-316,0.0,1.80516093e-316,3.56856976e-3
16,5.5126066e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems
.var"#f#1329"{Float64}, Float64}}(6.903326239131e-310,6.95258723262955e-310
,5.48817487e-316,NaN,0.0,5.48817605e-316,6.903326239131e-310,6.952587232629
55e-310,3.04932613e-316,NaN,0.0,3.0493273e-316,6.903326239131e-310), Dual{F
orwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Fl
oat64}}(3.83410524e-316,3.5846577e-316,7.5356833e-316,3.56856976e-316,3.584
6589e-316,6.903326239131e-310,3.8347171e-316,0.0,6.54488524e-316,3.56856976
e-316,6.39677147e-316,6.903326239131e-310,3.83411473e-316), Dual{ForwardDif
f.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(5
.488246e-316,5.4748007e-316,3.56856976e-316,5.4882472e-316,6.903326239131e-
310,3.8341171e-316,3.58468223e-316,3.8558472e-316,3.56856976e-316,3.5846834
e-316,6.903326239131e-310,3.8347266e-316,4.08116524e-316), Dual{ForwardDiff
.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(3.
12842486e-316,3.56856976e-316,4.0811664e-316,6.903326239131e-310,1.0e-323,0
.0,NaN,0.0,0.0,6.903326239131e-310,3.8347242e-316,0.0,6.3329643e-316), Dual
{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, 
Float64}}(3.56856976e-316,6.44383577e-316,6.903326239131e-310,3.8347337e-31
6,0.0,1.66409926e-316,3.56856976e-316,6.4438484e-316,6.903326239131e-310,1.
0e-323,0.0,NaN,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblem
s.var"#f#1329"{Float64}, Float64}}(0.0,6.903326239131e-310,3.8347313e-316,7
.9497364e-316,2.15861707e-316,3.56856976e-316,7.9497376e-316,6.903326239131
e-310,3.8347408e-316,4.0811605e-316,7.08022276e-316,3.56856976e-316,4.08116
17e-316), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#13
29"{Float64}, Float64}}(6.903326239131e-310,3.8347432e-316,0.0,4.5738969e-3
16,3.56856976e-316,6.7564054e-316,6.903326239131e-310,6.9525872325323e-310,
0.0,NaN,0.0,7.94976683e-316,6.903326239131e-310), Dual{ForwardDiff.Tag{Opti
mizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.952587232
62955e-310,0.0,NaN,0.0,9.85104843e-316,6.903326239131e-310,1.0e-323,0.0,NaN
,0.0,3.0492301e-316,6.903326239131e-310,6.95258723262955e-310), Dual{Forwar
dDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64
}}(0.0,NaN,0.0,2.22941787e-316,6.903326239131e-310,1.0e-323,0.0,NaN,0.0,0.0
,6.903326239131e-310,1.0e-323,0.0), Dual{ForwardDiff.Tag{OptimizationProble
ms.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(NaN,0.0,0.0,6.90332623913
1e-310,3.83415267e-316,0.0,6.4685509e-316,3.56856976e-316,7.94988936e-316,6
.903326239131e-310,3.83415504e-316,2.22941194e-316,7.35475923e-316), Dual{F
orwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Fl
oat64}}(3.56856976e-316,2.22941312e-316,6.903326239131e-310,3.8347645e-316,
6.44383933e-316,6.46835724e-316,3.56856976e-316,6.4438405e-316,6.9033262391
31e-310,3.8347669e-316,0.0,3.16568966e-316,3.56856976e-316), Dual{ForwardDi
ff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(
6.1593662e-316,6.903326239131e-310,3.8341574e-316,0.0,5.47481415e-316,3.568
56976e-316,5.48825194e-316,6.903326239131e-310,6.95258723265248e-310,6.9525
872326769e-310,NaN,0.0,6.15934566e-316), Dual{ForwardDiff.Tag{OptimizationP
roblems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(6.903326239131e-310,
3.8341598e-316,5.48823653e-316,8.271583e-316,3.56856976e-316,5.4882377e-316
,6.903326239131e-310,3.83416927e-316,7.94988343e-316,6.46855644e-316,3.5685
6976e-316,7.9498846e-316,6.079e-320), Dual{ForwardDiff.Tag{OptimizationProb
lems.ADNLPProblems.var"#f#1329"{Float64}, Float64}}(2.22e-321,5.1502794e-31
6,5.5114485e-316,5.5106082e-316,0.0,NaN,0.0,5.0e-324,0.0,6.7508549e-316,0.0
,1.6e-322,9.443317726047391e21), Dual{ForwardDiff.Tag{OptimizationProblems.
ADNLPProblems.var"#f#1329"{Float64}, Float64}}(7.558125123061879e-154,3.398
235778115e-312,7.8551510299e-313,6.75085725e-316,8.487983164e-314,-1.105587
1916232541e-244,-2.986397015342954e-254,1.2989153463666738e287,5.8801323708
32126e137,1.268934864557806e-231,-1.692812158093192e306,3.910462211847e-312
,2.42280991429251e-309), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPPro
blems.var"#f#1329"{Float64}, Float64}}(-1.8370094195097775e282,-9.782954743
948183e26,1.33586203965988e-309,2.736761793400046e44,1.033e-321,6.903327377
96695e-310,6.90332737796695e-310,3.7167341292703204e-268,1.1553676697937789
e48,1.19786786865135e-309,3.79171665626112e-309,-9.277781942621371e-299,7.8
52738716730545e42)])), ADNLPModels.ForwardDiffADHvprod(), ADNLPModels.Forwa
rdDiffADJprod(), ADNLPModels.ForwardDiffADJtprod(), ADNLPModels.ForwardDiff
ADJacobian(0), ADNLPModels.ForwardDiffADHessian(7260), ADNLPModels.ForwardD
iffADGHjvprod())
  Problem name: woods
   All variables: ████████████████████ 120    All constraints: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            free: ████████████████████ 120               free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   7260            linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                         nnzj: (------% spa
rsity)         

  Counters:
             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0

One of the advantages of these problems is that they are type-stable. Indeed, one can specify the output type with the keyword type as follows.

nlp16_12 = OptimizationProblems.ADNLPProblems.woods(n=12, type=Val(Float16))
ADNLPModel - Model with automatic differentiation backend ADNLPModels.ADMod
elBackend{ADNLPModels.ForwardDiffADGradient, ADNLPModels.ForwardDiffADHvpro
d, ADNLPModels.ForwardDiffADJprod, ADNLPModels.ForwardDiffADJtprod, ADNLPMo
dels.ForwardDiffADJacobian, ADNLPModels.ForwardDiffADHessian, ADNLPModels.F
orwardDiffADGHjvprod}(ADNLPModels.ForwardDiffADGradient(ForwardDiff.Gradien
tConfig{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Flo
at16}, Float16}, Float16, 12, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optim
izationProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}, Float16, 12}
}}((Partials(Float16(1.0), Float16(0.0), Float16(0.0), Float16(0.0), Float1
6(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0
), Float16(0.0), Float16(0.0)), Partials(Float16(0.0), Float16(1.0), Float1
6(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0
), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)), Partials(Float1
6(0.0), Float16(0.0), Float16(1.0), Float16(0.0), Float16(0.0), Float16(0.0
), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Fl
oat16(0.0)), Partials(Float16(0.0), Float16(0.0), Float16(0.0), Float16(1.0
), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Fl
oat16(0.0), Float16(0.0), Float16(0.0)), Partials(Float16(0.0), Float16(0.0
), Float16(0.0), Float16(0.0), Float16(1.0), Float16(0.0), Float16(0.0), Fl
oat16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)), Partia
ls(Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Fl
oat16(1.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16
(0.0), Float16(0.0)), Partials(Float16(0.0), Float16(0.0), Float16(0.0), Fl
oat16(0.0), Float16(0.0), Float16(0.0), Float16(1.0), Float16(0.0), Float16
(0.0), Float16(0.0), Float16(0.0), Float16(0.0)), Partials(Float16(0.0), Fl
oat16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16
(0.0), Float16(1.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)
), Partials(Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16
(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(1.0), Float16(0.0)
, Float16(0.0), Float16(0.0)), Partials(Float16(0.0), Float16(0.0), Float16
(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)
, Float16(0.0), Float16(1.0), Float16(0.0), Float16(0.0)), Partials(Float16
(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)
, Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(1.0), Flo
at16(0.0)), Partials(Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0)
, Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Float16(0.0), Flo
at16(0.0), Float16(0.0), Float16(1.0))), ForwardDiff.Dual{ForwardDiff.Tag{O
ptimizationProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}, Float16,
 12}[Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{F
loat16}, Float16}}(-2.344,0.3552,NaN,0.0,-2.469,0.3552,NaN,0.0,-2.594,0.355
2,NaN,0.0,-2.719), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.
var"#f#1329"{Float16}, Float16}}(0.3552,NaN,0.0,-2.844,0.3552,NaN,0.0,-2.96
9,0.3552,NaN,0.0,-3.094,0.3552), Dual{ForwardDiff.Tag{OptimizationProblems.
ADNLPProblems.var"#f#1329"{Float16}, Float16}}(NaN,0.0,-3.219,0.3552,NaN,0.
0,-3.344,0.3552,NaN,0.0,-3.469,0.3552,NaN), Dual{ForwardDiff.Tag{Optimizati
onProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}}(0.0,-3.594,0.3552
,NaN,0.0,-3.719,0.3552,NaN,0.0,-3.844,0.3552,NaN,0.0), Dual{ForwardDiff.Tag
{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}}(-3.969
,0.3552,NaN,0.0,-4.188,0.3552,NaN,0.0,-4.438,0.3552,NaN,0.0,-4.688), Dual{F
orwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float16}, Fl
oat16}}(0.3552,NaN,0.0,-4.938,0.3552,NaN,0.0,-5.188,0.3552,NaN,0.0,-5.438,0
.3552), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329
"{Float16}, Float16}}(NaN,0.0,-5.688,0.3552,NaN,0.0,-5.938,0.3552,NaN,0.0,-
6.188,0.3552,NaN), Dual{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.
var"#f#1329"{Float16}, Float16}}(0.0,-6.438,0.3552,NaN,0.0,-6.688,0.3552,Na
N,0.0,-6.938,0.3552,NaN,0.0), Dual{ForwardDiff.Tag{OptimizationProblems.ADN
LPProblems.var"#f#1329"{Float16}, Float16}}(-7.188,0.3552,NaN,0.0,-7.438,0.
3552,NaN,0.0,-7.688,0.3552,NaN,0.0,-7.938), Dual{ForwardDiff.Tag{Optimizati
onProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}}(0.3552,NaN,0.0,-8
.375,0.3552,NaN,0.0,-8.875,0.3552,NaN,0.0,-9.375,0.3552), Dual{ForwardDiff.
Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float16}, Float16}}(NaN
,0.0,-9.875,0.3552,NaN,0.0,-10.375,0.3552,NaN,0.0,-10.875,0.3552,NaN), Dual
{ForwardDiff.Tag{OptimizationProblems.ADNLPProblems.var"#f#1329"{Float16}, 
Float16}}(0.0,-11.375,0.3552,NaN,0.0,-13.5,-4.42e3,NaN,0.0,-12.0,-0.02345,N
aN,0.0)])), ADNLPModels.ForwardDiffADHvprod(), ADNLPModels.ForwardDiffADJpr
od(), ADNLPModels.ForwardDiffADJtprod(), ADNLPModels.ForwardDiffADJacobian(
0), ADNLPModels.ForwardDiffADHessian(78), ADNLPModels.ForwardDiffADGHjvprod
())
  Problem name: woods
   All variables: ████████████████████ 12     All constraints: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            free: ████████████████████ 12                free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   78              linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                         nnzj: (------% spa
rsity)         

  Counters:
             obj: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 grad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 cons: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ 0

Then, all the API will be compatible with the precised type.

using NLPModels
obj(nlp16_12, zeros(Float16, 12))
Float16(126.0)