Performance tips

The package ADNLPModels.jl is designed to easily model optimization problems andto allow an efficient access to the NLPModel API. In this tutorial, we will see some tips to ensure the maximum performance of the model.

Use in-place constructor

When dealing with a constrained optimization problem, it is recommended to use in-place constraint functions.

using ADNLPModels, NLPModels
f(x) = sum(x)
x0 = ones(2)
lcon = ucon = ones(1)
c_out(x) = [x[1]]
nlp_out = ADNLPModel(f, x0, c_out, lcon, ucon)

c_in(cx, x) = begin
  cx[1] = x[1]
  return cx
end
nlp_in = ADNLPModel!(f, x0, c_in, lcon, ucon)

ADNLPModel - Model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  SparseADJacobian,
  SparseADHessian,
  ForwardDiffADGHjvprod,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ████████████████████ 1     
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████████████ 1     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (100.00% sparsity)   0               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ████████████████████ 1     
                                                         nnzj: ( 50.00% sparsity)   1     

  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

using BenchmarkTools
cx = rand(1)
x = 18 * ones(2)
@btime cons!(nlp_out, x, cx)

1-element Vector{Float64}:
 18.0

@btime cons!(nlp_in, x, cx)

1-element Vector{Float64}:
 18.0

The difference between the two increases with the dimension.

Note that the same applies to nonlinear least squares problems.

F(x) = [
    x[1];
    x[1] + x[2]^2;
    sin(x[2]);
    exp(x[1] + 0.5)
]
x0 = ones(2)
nequ = 4
nls_out = ADNLSModel(F, x0, nequ)

F!(Fx, x) = begin
  Fx[1] = x[1]
  Fx[2] = x[1] + x[2]^2
  Fx[3] = sin(x[2])
  Fx[4] = exp(x[1] + 0.5)
  return Fx
end
nls_in = ADNLSModel!(F!, x0, nequ)

ADNLSModel - Nonlinear least-squares model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  EmptyADbackend,
  EmptyADbackend,
  EmptyADbackend,
  SparseADHessian,
  EmptyADbackend,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  SparseADJacobian,
  SparseADHessian,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0        All residuals: ████████████████████ 4     
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0            nonlinear: ████████████████████ 4     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 nnzj: ( 37.50% sparsity)   5     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 nnzh: ( 33.33% sparsity)   2     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   3               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                         nnzj: (------% sparsity)         

  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             residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
    jac_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0       jprod_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0      jtprod_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
   hess_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0       jhess_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0       hprod_residual: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0

Fx = rand(4)
@btime residual!(nls_out, x, Fx)

4-element Vector{Float64}:
  18.0
 342.0
  -0.7509872467716762
   1.0825498775023076e8

@btime residual!(nls_in, x, Fx)

4-element Vector{Float64}:
  18.0
 342.0
  -0.7509872467716762
   1.0825498775023076e8

This phenomenon also extends to related backends.

Fx = rand(4)
v = ones(2)
@btime jprod_residual!(nls_out, x, v, Fx)

4-element Vector{Float64}:
  1.0
 37.0
  0.6603167082440802
  1.0825498775023076e8

@btime jprod_residual!(nls_in, x, v, Fx)

4-element Vector{Float64}:
  1.0
 37.0
  0.6603167082440802
  1.0825498775023076e8

Use only the needed operations

It is tempting to define the most generic and efficient ADNLPModel from the start.

using ADNLPModels, NLPModels
f(x) = (x[1] - x[2])^2
x0 = ones(2)
lcon = ucon = ones(1)
c_in(cx, x) = begin
  cx[1] = x[1]
  return cx
end
nlp = ADNLPModel!(f, x0, c_in, lcon, ucon, show_time = true)

ADNLPModel - Model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  SparseADJacobian,
  SparseADHessian,
  ForwardDiffADGHjvprod,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ████████████████████ 1     
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████████████ 1     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   3               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ████████████████████ 1     
                                                         nnzj: ( 50.00% sparsity)   1     

  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

However, depending on the size of the problem this might time consuming as initializing each backend takes time. Besides, some solvers may not require all the API to solve the problem. For instance, Percival.jl is matrix-free solver in the sense that it only uses jprod, jtprod and hprod.

using Percival
stats = percival(nlp)

"Execution stats: first-order stationary"

nlp.counters

  Counters:
             obj: ████████████████████ 1                 grad: ████████████████████ 1                 cons: ████████████████████ 1     
        cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0             cons_nln: ████████████████████ 1                 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                  jac: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0            jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
       jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jtprod: ████████████████████ 1           jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
      jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                 hess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0

Therefore, it is more efficient to avoid preparing Jacobian and Hessian backends in this case.

nlp = ADNLPModel!(f, x0, c_in, lcon, ucon, jacobian_backend = ADNLPModels.EmptyADbackend, hessian_backend = ADNLPModels.EmptyADbackend, show_time = true)

ADNLPModel - Model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  EmptyADbackend,
  EmptyADbackend,
  ForwardDiffADGHjvprod,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ████████████████████ 1     
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████████████ 1     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   3               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ████████████████████ 1     
                                                         nnzj: (  0.00% sparsity)   2     

  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

or, equivalently, using the matrix_free keyword argument

nlp = ADNLPModel!(f, x0, c_in, lcon, ucon, show_time = true, matrix_free = true)

ADNLPModel - Model with automatic differentiation backend ADModelBackend{
  ForwardDiffADGradient,
  ForwardDiffADHvprod,
  ForwardDiffADJprod,
  ForwardDiffADJtprod,
  EmptyADbackend,
  EmptyADbackend,
  ForwardDiffADGHjvprod,
}
  Problem name: Generic
   All variables: ████████████████████ 2      All constraints: ████████████████████ 1     
            free: ████████████████████ 2                 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
         low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0              low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
           fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0                fixed: ████████████████████ 1     
          infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0               infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
            nnzh: (  0.00% sparsity)   3               linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0     
                                                    nonlinear: ████████████████████ 1     
                                                         nnzj: (  0.00% sparsity)   2     

  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

Benchmarks

This package implements several backends for each method and it is possible to design your own backend as well. Then, one way to choose the most efficient one is to run benchmarks.

using ADNLPModels, NLPModels, OptimizationProblems

The package OptimizationProblems.jl provides a collection of optimization problems in JuMP and ADNLPModels syntax.

meta = OptimizationProblems.meta;

372×17 DataFrame

Row	nvar	variable_nvar	ncon	variable_ncon	minimize	name	has_equalities_only	has_inequalities_only	has_bounds	has_fixed_variables	objtype	contype	best_known_lower_bound	best_known_upper_bound	is_feasible	defined_everywhere	origin
	Int64	Bool	Int64	Bool	Bool	String	Bool	Bool	Bool	Bool	Symbol	Symbol	Real	Real	Bool?	Bool?	Symbol
1	1	false	0	false	true	AMPGO02	false	false	false	false	other	unconstrained	-Inf	0.839498	true	missing	unknown
2	1	false	0	false	true	AMPGO03	false	false	false	false	other	unconstrained	-Inf	2.88961	true	missing	unknown
3	1	false	0	false	true	AMPGO04	false	false	false	false	other	unconstrained	-Inf	-2.5666	true	missing	unknown
4	1	false	0	false	true	AMPGO05	false	false	false	false	other	unconstrained	-Inf	-0.0	true	missing	unknown
5	1	false	0	false	true	AMPGO06	false	false	false	false	other	unconstrained	-Inf	3.5177e-43	true	missing	unknown
6	1	false	0	false	true	AMPGO07	false	false	false	false	other	unconstrained	-Inf	2.56475	true	missing	unknown
7	1	false	0	false	true	AMPGO08	false	false	false	false	other	unconstrained	-Inf	-2.0928	true	missing	unknown
8	1	false	0	false	true	AMPGO09	false	false	false	false	other	unconstrained	-Inf	0.921136	true	missing	unknown
9	1	false	0	false	true	AMPGO10	false	false	false	false	other	unconstrained	-Inf	-0.0	true	missing	unknown
10	1	false	0	false	true	AMPGO11	false	false	false	false	other	unconstrained	-Inf	-1.0	true	missing	unknown
11	1	false	0	false	true	AMPGO12	false	false	false	false	other	unconstrained	-Inf	1.0	true	missing	unknown
12	1	false	0	false	true	AMPGO13	false	false	false	false	other	unconstrained	-1.5874	-1.5874	true	missing	unknown
13	1	false	0	false	true	AMPGO14	false	false	false	false	other	unconstrained	-Inf	-0.0	true	missing	unknown
14	1	false	0	false	true	AMPGO15	false	false	false	false	other	unconstrained	-Inf	2.15385	true	missing	unknown
15	1	false	0	false	true	AMPGO18	false	false	false	false	other	unconstrained	-Inf	4.0	true	missing	unknown
16	1	false	0	false	true	AMPGO20	false	false	false	false	other	unconstrained	-Inf	3.92246e-43	true	missing	unknown
17	1	false	0	false	true	AMPGO21	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
18	1	false	0	false	true	AMPGO22	false	false	false	false	other	unconstrained	-Inf	1.0	true	missing	unknown
19	3	false	1	false	true	BOX2	true	false	false	false	other	linear	-Inf	0.942284	true	missing	unknown
20	3	false	0	false	true	BOX3	false	false	false	false	other	unconstrained	-Inf	662.868	true	missing	unknown
21	1	false	0	false	true	Dus2_1	false	false	false	false	other	unconstrained	-Inf	7.38906	true	missing	unknown
22	1	false	0	false	true	Dus2_3	false	false	false	false	other	unconstrained	-Inf	0.972973	true	missing	unknown
23	1	false	0	false	true	Dus2_9	false	false	false	false	other	unconstrained	-Inf	1.0	true	missing	unknown
24	1	false	0	false	true	Duscube	false	false	false	false	other	unconstrained	-Inf	-108.0	true	missing	unknown
25	91	true	0	false	true	NZF1	false	false	false	false	least_squares	unconstrained	-Inf	34698.4	true	missing	unknown
26	1	false	0	false	true	Shpak1	false	false	false	false	other	unconstrained	-Inf	0.839498	true	missing	unknown
27	1	false	0	false	true	Shpak2	false	false	false	false	other	unconstrained	-Inf	-0.747036	true	missing	unknown
28	1	false	0	false	true	Shpak3	false	false	false	false	other	unconstrained	-Inf	2.63055	true	missing	unknown
29	1	false	0	false	true	Shpak4	false	false	false	false	other	unconstrained	-Inf	-0.677439	true	missing	unknown
30	1	false	0	false	true	Shpak5	false	false	false	false	other	unconstrained	-Inf	-1.00842	true	missing	unknown
31	1	false	0	false	true	Shpak6	false	false	false	false	other	unconstrained	-Inf	-1.25667	true	missing	unknown
32	8	false	5	false	true	aircrfta	true	false	true	true	other	general	-Inf	0	true	missing	unknown
33	4	false	3	false	true	allinit	false	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
34	4	false	4	false	true	allinitc	false	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
35	4	false	0	false	true	allinitu	false	false	false	false	other	unconstrained	-Inf	13.0	true	missing	unknown
36	2	false	3	false	true	alsotame	false	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
37	3	false	15	false	true	argauss	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
38	100	true	0	false	true	arglina	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
39	100	true	0	false	true	arglinb	false	false	false	false	least_squares	unconstrained	-Inf	6.85174e13	true	missing	unknown
40	100	true	0	false	true	arglinc	false	false	false	false	other	unconstrained	-Inf	6.38544e13	true	missing	unknown
41	100	true	0	false	true	argtrig	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
42	100	true	0	false	true	arwhead	false	false	false	false	other	unconstrained	-Inf	297.0	true	missing	unknown
43	49	false	15	false	true	avion2	true	false	true	false	least_squares	general	-Inf	Inf	missing	missing	unknown
44	3	false	0	false	true	bard	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
45	100	true	0	false	true	bdqrtic	false	false	false	false	least_squares	unconstrained	-Inf	21696.0	true	missing	unknown
46	2	false	0	false	true	beale	false	false	false	false	least_squares	unconstrained	-Inf	14.2031	true	missing	unknown
47	100	true	0	false	true	bearing	false	false	true	true	other	unconstrained	-Inf	15.0662	true	missing	unknown
48	3	false	0	false	true	bennett5	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
49	6	false	0	false	true	biggs5	false	false	true	true	other	unconstrained	-Inf	-3.15621	true	missing	unknown
50	6	false	0	false	true	biggs6	false	false	false	false	other	unconstrained	-Inf	-3.15621	true	missing	unknown
51	2	false	2	false	true	booth	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
52	2	false	0	false	true	boxbod	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
53	1	false	1	false	true	bqp1var	false	true	false	false	other	general	-Inf	0.3125	true	missing	unknown
54	450	false	360	false	true	britgas	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
55	100	true	0	false	true	brownal	false	false	false	false	least_squares	unconstrained	-Inf	0.0	true	missing	unknown
56	2	false	0	false	true	brownbs	false	false	false	false	least_squares	unconstrained	-Inf	9.99998e11	true	missing	unknown
57	4	false	0	false	true	brownden	false	false	false	false	least_squares	unconstrained	-Inf	7.92669e6	true	missing	unknown
58	100	true	0	false	true	broyden3d	false	false	false	false	least_squares	unconstrained	-Inf	0.0	true	missing	unknown
59	100	true	0	false	true	broydn7d	false	false	false	false	other	unconstrained	-Inf	274.204	true	missing	unknown
60	100	true	0	false	true	brybnd	false	false	false	false	least_squares	unconstrained	-Inf	3600.0	true	missing	unknown
61	2	false	1	false	true	bt1	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
62	100	true	203	true	true	camshape	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
63	99	true	32	true	true	catenary	true	false	true	true	linear	quadratic	-Inf	Inf	missing	missing	academic
64	100	true	77	true	true	chain	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
65	100	true	0	false	true	chainwoo	false	false	false	false	other	unconstrained	-Inf	3.71954e5	true	missing	unknown
66	96	true	96	true	true	channel	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
67	100	true	0	false	true	chnrosnb_mod	false	false	false	false	other	unconstrained	-Inf	17637.9	true	missing	unknown
68	3	false	0	false	true	chwirut1	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
69	3	false	0	false	true	chwirut2	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
70	2	false	0	false	true	cliff	false	false	false	false	other	unconstrained	-Inf	4.85165e8	true	missing	unknown
71	99	true	64	true	true	clnlbeam	true	false	true	false	other	general	-Inf	350.0	true	missing	unknown
72	100	true	0	false	true	clplatea	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
73	100	true	0	false	true	clplateb	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
74	100	true	0	false	true	clplatec	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
75	100	true	50	true	true	controlinvestment	true	false	true	false	other	general	-Inf	-0.98	true	missing	unknown
76	100	true	0	false	true	cosine	false	false	false	false	other	unconstrained	-Inf	86.8807	true	missing	unknown
77	100	true	0	false	true	cragglvy	false	false	false	false	other	unconstrained	-Inf	52823.1	true	missing	unknown
78	100	true	0	false	true	cragglvy2	false	false	false	false	other	unconstrained	-Inf	52823.1	true	missing	unknown
79	100	true	0	false	true	curly	false	false	false	false	other	unconstrained	-Inf	-0.00623722	true	missing	unknown
80	100	true	0	false	true	curly10	false	false	false	false	other	unconstrained	-Inf	-0.00623722	true	missing	unknown
81	100	true	0	false	true	curly20	false	false	false	false	other	unconstrained	-Inf	-0.0129654	true	missing	unknown
82	100	true	0	false	true	curly30	false	false	false	false	other	unconstrained	-Inf	-0.020383	true	missing	unknown
83	2	false	0	false	true	danwood	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
84	99	true	0	false	true	dixmaane	false	false	false	false	other	unconstrained	-Inf	731.833	true	missing	unknown
85	99	true	0	false	true	dixmaanf	false	false	false	false	other	unconstrained	-Inf	1348.42	true	missing	unknown
86	99	true	0	false	true	dixmaang	false	false	false	false	other	unconstrained	-Inf	2495.83	true	missing	unknown
87	99	true	0	false	true	dixmaanh	false	false	false	false	other	unconstrained	-Inf	4974.25	true	missing	unknown
88	99	true	0	false	true	dixmaani	false	false	false	false	other	unconstrained	-Inf	663.646	true	missing	unknown
89	99	true	0	false	true	dixmaanj	false	false	false	false	other	unconstrained	-Inf	1281.33	true	missing	unknown
90	99	true	0	false	true	dixmaank	false	false	false	false	other	unconstrained	-Inf	2427.65	true	missing	unknown
91	99	true	0	false	true	dixmaanl	false	false	false	false	other	unconstrained	-Inf	4903.7	true	missing	unknown
92	99	true	0	false	true	dixmaanm	false	false	false	false	other	unconstrained	-Inf	314.313	true	missing	unknown
93	99	true	0	false	true	dixmaann	false	false	false	false	other	unconstrained	-Inf	665.66	true	missing	unknown
94	99	true	0	false	true	dixmaano	false	false	false	false	other	unconstrained	-Inf	1196.31	true	missing	unknown
95	99	true	0	false	true	dixmaanp	false	false	false	false	other	unconstrained	-Inf	2342.52	true	missing	unknown
96	100	true	0	false	true	dixon3dq	false	false	false	false	least_squares	unconstrained	-Inf	8.0	true	missing	unknown
97	100	true	0	false	true	dqdrtic	false	false	false	false	other	unconstrained	-Inf	177282.0	true	missing	unknown
98	100	true	0	false	true	dqrtic	false	false	false	false	other	unconstrained	-Inf	1.85427e9	true	missing	unknown
99	3	false	0	false	true	eckerle4	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
100	100	true	0	false	true	edensch	false	false	false	false	other	unconstrained	-Inf	1699.0	true	missing	unknown
101	100	true	0	false	true	eg2	false	false	false	false	other	unconstrained	-Inf	-83.3056	true	missing	unknown
102	99	true	33	true	true	elec	true	false	false	false	other	quadratic	-Inf	Inf	missing	missing	unknown
103	100	true	0	false	true	engval1	false	false	false	false	other	unconstrained	-Inf	5841.0	true	missing	unknown
104	9	false	0	false	true	enso	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
105	100	true	0	false	true	errinros_mod	false	false	false	false	least_squares	unconstrained	-Inf	3.13991e5	true	missing	unknown
106	100	true	0	false	true	extrosnb	false	false	false	false	other	unconstrained	-Inf	39604.0	true	missing	unknown
107	100	true	0	false	true	fletcbv2	false	false	false	false	other	unconstrained	-Inf	-0.513108	true	missing	unknown
108	100	true	0	false	true	fletcbv3_mod	false	false	false	false	other	unconstrained	-Inf	-0.0187925	true	missing	unknown
109	100	true	0	false	true	fletchcr	false	false	false	false	other	unconstrained	-Inf	9900.0	true	missing	unknown
110	100	false	0	false	true	fminsrf2	false	false	false	false	other	unconstrained	-Inf	2504.27	true	missing	unknown
111	100	true	0	false	true	freuroth	false	false	false	false	least_squares	unconstrained	-Inf	99556.5	true	missing	unknown
112	8	false	0	false	true	gauss1	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
113	8	false	0	false	true	gauss2	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
114	8	false	0	false	true	gauss3	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
115	3	false	0	false	true	gaussian	false	false	false	false	least_squares	unconstrained	-Inf	3.88811e-6	true	missing	unknown
116	100	true	0	false	true	genhumps	false	false	false	false	other	unconstrained	-Inf	2.53684e6	true	missing	unknown
117	100	true	0	false	true	genrose	false	false	false	false	other	unconstrained	-Inf	405.106	true	missing	unknown
118	100	true	0	false	true	genrose_nash	false	false	false	false	other	unconstrained	-Inf	404.126	true	missing	unknown
119	3	false	0	false	true	gulf	false	false	false	false	least_squares	unconstrained	-Inf	0.0	true	missing	unknown
120	7	false	0	false	true	hahn1	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
121	3	false	0	false	true	helical	false	false	false	false	other	unconstrained	-Inf	0.0	true	missing	unknown
122	98	true	68	true	true	hovercraft1d	true	false	false	false	least_squares	linear	-Inf	Inf	missing	missing	unknown
123	2	false	0	false	true	hs1	false	false	true	false	other	unconstrained	-Inf	909.0	true	missing	unknown
124	2	false	1	false	true	hs10	false	true	false	false	other	general	-Inf	Inf	missing	missing	unknown
125	7	false	4	false	true	hs100	false	true	false	false	other	general	-Inf	714.0	true	missing	unknown
126	7	false	5	false	true	hs101	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
127	7	false	5	false	true	hs102	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
128	7	false	5	false	true	hs103	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
129	8	false	5	false	true	hs104	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
130	8	false	1	false	true	hs105	false	true	true	false	other	linear	-Inf	Inf	missing	missing	unknown
131	8	false	6	false	true	hs106	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
132	9	false	6	false	true	hs107	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
133	9	false	12	false	true	hs108	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
134	9	false	9	false	true	hs109	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
135	2	false	1	false	true	hs11	false	true	false	false	other	general	-Inf	Inf	missing	missing	unknown
136	10	false	0	false	true	hs110	false	false	true	false	other	unconstrained	-Inf	-43.1343	true	missing	unknown
137	10	false	3	false	true	hs111	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
138	10	false	3	false	true	hs112	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
139	10	false	8	false	true	hs113	false	true	false	false	other	general	-Inf	753.0	true	missing	unknown
140	10	false	11	false	true	hs114	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
141	13	false	15	false	true	hs116	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
142	15	false	5	false	true	hs117	false	true	true	false	other	general	-Inf	2400.11	true	missing	unknown
143	15	false	17	false	true	hs118	false	true	true	false	other	linear	-Inf	942.716	true	missing	unknown
144	16	false	8	false	true	hs119	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
145	2	false	1	false	true	hs12	false	true	false	false	other	general	-Inf	0.0	true	missing	unknown
146	2	false	1	false	true	hs13	false	true	true	false	least_squares	general	-Inf	Inf	missing	missing	unknown
147	2	false	2	false	true	hs14	false	false	false	false	least_squares	general	-Inf	Inf	missing	missing	unknown
148	2	false	2	false	true	hs15	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
149	2	false	2	false	true	hs16	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
150	2	false	2	false	true	hs17	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
151	2	false	2	false	true	hs18	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
152	2	false	2	false	true	hs19	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
153	2	false	0	false	true	hs2	false	false	true	false	other	unconstrained	-Inf	909.0	true	missing	unknown
154	2	false	3	false	true	hs20	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
155	2	false	1	false	true	hs21	false	true	true	false	other	linear	-Inf	Inf	missing	missing	unknown
156	4	false	2	false	true	hs219	true	false	false	false	linear	general	-1.0	-1.0	true	true	unknown
157	2	false	2	false	true	hs22	false	true	false	false	least_squares	general	-Inf	Inf	missing	missing	unknown
158	2	false	1	false	true	hs220	true	false	true	false	other	general	1	25000	true	missing	unknown
159	2	false	1	false	true	hs221	false	true	true	false	other	general	-1	-0.25	true	missing	unknown
160	2	false	1	false	true	hs222	false	true	true	false	other	general	-1.5	-1.3	true	missing	unknown
161	2	false	2	false	true	hs223	false	true	true	false	other	general	-0.834032	-0.1	true	missing	unknown
162	2	false	4	false	true	hs224	false	true	true	false	other	linear	-304	-304	true	missing	unknown
163	2	false	5	false	true	hs225	false	true	false	false	other	general	2	2	true	missing	unknown
164	2	false	2	false	true	hs226	false	true	true	false	other	general	-0.5	-0.5	true	missing	unknown
165	2	false	2	false	true	hs227	false	true	false	false	other	general	1	1	true	missing	unknown
166	2	false	2	false	true	hs228	false	true	false	false	other	general	-3	-3	true	missing	unknown
167	2	false	0	false	true	hs229	false	false	true	false	other	unconstrained	0	0	true	missing	unknown
168	2	false	5	false	true	hs23	false	true	true	false	least_squares	general	-Inf	Inf	missing	missing	unknown
169	2	false	2	false	true	hs230	false	true	false	false	other	general	0.375	0.375	true	missing	unknown
170	2	false	2	false	true	hs231	false	true	false	false	other	linear	0	0	true	missing	unknown
171	2	false	3	false	true	hs232	false	true	true	false	other	linear	-1	-1	true	missing	unknown
172	2	false	1	false	true	hs233	false	true	false	false	other	unconstrained	0	0	true	missing	unknown
173	2	false	1	false	true	hs234	false	true	true	false	other	general	-0.8	-0.8	true	missing	unknown
174	3	false	1	false	true	hs235	true	false	false	false	other	general	0.04	0.04	true	missing	unknown
175	2	false	2	false	true	hs236	false	true	true	false	other	general	-58.9034	-58.9034	true	missing	unknown
176	2	false	3	false	true	hs237	false	true	true	false	other	general	-58.9034	-58.9034	true	missing	unknown
177	2	false	3	false	true	hs238	false	true	true	false	other	general	-58.9034	-58.9034	true	missing	unknown
178	2	false	1	false	true	hs239	false	true	true	false	other	general	-58.9034	-58.9034	true	missing	unknown
179	2	false	2	false	true	hs24	false	true	true	false	other	linear	-Inf	-0.0133646	true	missing	unknown
180	3	false	0	false	true	hs240	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
181	3	false	0	false	true	hs241	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
182	3	false	0	false	true	hs242	false	false	true	false	other	unconstrained	0	0	true	missing	unknown
183	3	false	0	false	true	hs243	false	false	false	false	other	unconstrained	0.7966	0.7966	true	missing	unknown
184	3	false	0	false	true	hs244	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
185	3	false	0	false	true	hs245	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
186	3	false	0	false	true	hs246	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
187	3	false	2	false	true	hs248	false	false	false	false	other	general	-0.8	-0.8	true	missing	unknown
188	3	false	1	false	true	hs249	false	true	true	false	other	general	1	1	true	missing	unknown
189	3	false	0	false	true	hs25	false	false	true	false	other	unconstrained	-Inf	32.835	true	missing	unknown
190	3	false	2	false	true	hs250	false	true	true	false	other	linear	-3300	-3300	true	missing	unknown
191	3	false	1	false	true	hs251	false	true	true	false	other	linear	-3456	-3456	true	missing	unknown
192	3	false	1	false	true	hs252	true	false	false	false	other	unconstrained	0.04	0.04	true	missing	unknown
193	3	false	1	false	true	hs253	false	true	true	false	other	linear	87.3794	87.3794	true	missing	unknown
194	3	false	2	false	true	hs254	true	false	true	false	other	general	-1.73205	-1.73205	true	missing	unknown
195	4	false	0	false	true	hs255	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
196	4	false	0	false	true	hs256	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
197	4	false	0	false	true	hs257	false	false	true	false	other	unconstrained	0	0	true	missing	unknown
198	4	false	0	false	true	hs258	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
199	4	false	0	false	true	hs259	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
200	3	false	1	false	true	hs26	true	false	false	false	other	general	-Inf	21.16	true	missing	unknown
201	4	false	0	false	true	hs260	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
202	4	false	0	false	true	hs261	false	false	false	false	other	unconstrained	0	0	true	missing	unknown
203	4	false	4	false	true	hs262	false	false	true	false	other	linear	-10	-10	true	missing	unknown
204	4	false	4	false	true	hs263	false	false	false	false	other	general	-1	-1	true	missing	unknown
205	4	false	3	false	true	hs264	false	true	false	false	other	general	-44	-44	true	missing	unknown
206	4	false	2	false	true	hs265	true	false	true	false	other	linear	0.974747	0.974747	true	missing	unknown
207	3	false	1	false	true	hs27	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
208	3	false	1	false	true	hs28	true	false	false	false	least_squares	linear	-Inf	13.0	true	missing	unknown
209	3	false	1	false	true	hs29	false	true	false	false	other	general	-Inf	-1.0	true	missing	unknown
210	2	false	0	false	true	hs3	false	false	true	false	other	unconstrained	-Inf	1.00081	true	missing	unknown
211	3	false	1	false	true	hs30	false	true	true	false	least_squares	general	-Inf	3.0	true	missing	unknown
212	3	false	1	false	true	hs31	false	true	true	false	other	general	-Inf	19.0	true	missing	unknown
213	2	false	1	false	true	hs316	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
214	2	false	1	false	true	hs317	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
215	2	false	1	false	true	hs318	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
216	2	false	1	false	true	hs319	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
217	3	false	2	false	true	hs32	false	false	true	false	other	general	-Inf	7.2	true	missing	unknown
218	2	false	1	false	true	hs320	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
219	2	false	1	false	true	hs321	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
220	2	false	1	false	true	hs322	true	false	false	false	quadratic	quadratic	-Inf	Inf	true	missing	academic
221	3	false	2	false	true	hs33	false	true	true	false	other	general	-Inf	-3.0	true	missing	unknown
222	3	false	2	false	true	hs34	false	true	true	false	other	general	-Inf	0.0	true	missing	unknown
223	3	false	1	false	true	hs35	false	true	true	false	other	linear	-Inf	2.25	true	missing	unknown
224	3	false	1	false	true	hs36	false	true	true	false	other	linear	-Inf	-1000.0	true	missing	unknown
225	3	false	1	false	true	hs37	false	true	true	false	other	linear	-Inf	-1000.0	true	missing	unknown
226	10	false	3	false	true	hs378	true	false	false	false	other	general	-Inf	Inf	true	missing	academic
227	4	false	0	false	true	hs38	false	false	true	false	other	unconstrained	-Inf	19192.0	true	missing	unknown
228	4	false	2	false	true	hs39	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
229	2	false	0	false	true	hs4	false	false	true	false	other	unconstrained	-Inf	3.32357	true	missing	unknown
230	4	false	3	false	true	hs40	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
231	4	false	1	false	true	hs41	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
232	4	false	2	false	true	hs42	true	false	false	false	least_squares	general	-Inf	Inf	missing	missing	unknown
233	4	false	3	false	true	hs43	false	true	false	false	other	general	-Inf	0.0	true	missing	unknown
234	4	false	6	false	true	hs44	false	true	true	false	other	linear	-Inf	0.0	true	missing	unknown
235	5	false	0	false	true	hs45	false	false	true	false	other	unconstrained	-Inf	1.73333	true	missing	unknown
236	5	false	2	false	true	hs46	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
237	5	false	3	false	true	hs47	true	false	false	false	other	general	-Inf	20.7381	true	missing	unknown
238	5	false	2	false	true	hs48	true	false	false	false	least_squares	linear	-Inf	84.0	true	missing	unknown
239	5	false	2	false	true	hs49	true	false	false	false	other	linear	-Inf	266.0	true	missing	unknown
240	2	false	0	false	true	hs5	false	false	true	false	other	unconstrained	-Inf	1.0	true	missing	unknown
241	5	false	3	false	true	hs50	true	false	false	false	other	linear	-Inf	7516.0	true	missing	unknown
242	5	false	3	false	true	hs51	true	false	false	false	least_squares	linear	-Inf	8.5	true	missing	unknown
243	5	false	3	false	true	hs52	true	false	false	false	least_squares	linear	-Inf	Inf	missing	missing	unknown
244	5	false	3	false	true	hs53	true	false	true	false	least_squares	linear	-Inf	Inf	missing	missing	unknown
245	6	false	1	false	true	hs54	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
246	6	false	6	false	true	hs55	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
247	7	false	4	false	true	hs56	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
248	2	false	1	false	true	hs57	false	true	true	false	least_squares	general	-Inf	0.0307986	true	missing	unknown
249	2	false	3	false	true	hs59	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
250	2	false	1	false	true	hs6	true	false	false	false	least_squares	general	-Inf	Inf	missing	missing	unknown
251	3	false	1	false	true	hs60	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
252	3	false	2	false	true	hs61	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
253	3	false	1	false	true	hs62	true	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
254	3	false	2	false	true	hs63	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
255	3	false	1	false	true	hs64	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
256	3	false	1	false	true	hs65	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
257	3	false	2	false	true	hs66	false	true	true	false	other	general	-Inf	0.58	true	missing	unknown
258	4	false	2	false	true	hs68	true	false	true	false	other	general	-Inf	Inf	true	missing	unknown
259	4	false	2	false	true	hs69	true	false	true	false	other	general	-Inf	Inf	true	missing	unknown
260	2	false	1	false	true	hs7	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
261	4	false	1	false	true	hs70	false	true	true	false	other	general	-Inf	0.987859	true	missing	unknown
262	4	false	2	false	true	hs71	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
263	4	false	2	false	true	hs72	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
264	4	false	3	false	true	hs73	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
265	4	false	4	false	true	hs74	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
266	4	false	4	false	true	hs75	false	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
267	4	false	3	false	true	hs76	false	true	true	false	other	linear	-Inf	-1.25	true	missing	unknown
268	5	false	2	false	true	hs77	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
269	5	false	3	false	true	hs78	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
270	5	false	3	false	true	hs79	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
271	2	false	2	false	true	hs8	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
272	5	false	3	false	true	hs80	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
273	5	false	3	false	true	hs81	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
274	5	false	3	false	true	hs83	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
275	5	false	3	false	true	hs84	false	true	true	false	other	general	-Inf	-2.35124e6	true	missing	unknown
276	5	false	10	false	true	hs86	false	true	true	false	other	linear	-Inf	20.0	true	missing	unknown
277	6	false	4	false	true	hs87	true	false	true	false	other	general	-Inf	Inf	true	missing	unknown
278	2	false	1	false	true	hs9	true	false	false	false	other	linear	-Inf	0.0	true	missing	unknown
279	6	false	2	false	true	hs93	false	true	true	false	other	general	-Inf	137.066	true	missing	unknown
280	6	false	4	false	true	hs95	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
281	6	false	4	false	true	hs96	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
282	6	false	4	false	true	hs97	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
283	6	false	4	false	true	hs98	false	true	true	false	other	general	-Inf	Inf	missing	missing	unknown
284	7	false	2	false	true	hs99	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
285	100	true	0	false	true	indef_mod	false	false	false	false	other	unconstrained	-Inf	91.6655	true	missing	unknown
286	100	true	0	false	true	integreq	false	false	false	false	least_squares	unconstrained	-Inf	0.0	true	missing	unknown
287	2	false	0	false	true	jennrichsampson	false	false	false	false	least_squares	unconstrained	-Inf	4171.31	true	missing	unknown
288	5	false	0	false	true	kirby2	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
289	4	false	0	false	true	kowosb	false	false	false	false	least_squares	unconstrained	-Inf	0.0264978	true	missing	unknown
290	6	false	0	false	true	lanczos1	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
291	6	false	0	false	true	lanczos2	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
292	6	false	0	false	true	lanczos3	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
293	100	true	0	false	true	liarwhd	false	false	false	false	other	unconstrained	-Inf	58500.0	true	missing	unknown
294	15	false	11	false	true	lincon	false	false	false	false	other	linear	-Inf	Inf	missing	missing	unknown
295	2	false	2	false	true	linsv	false	true	false	false	other	linear	-Inf	Inf	missing	missing	unknown
296	111	true	40	true	true	marine	true	false	true	false	other	general	-Inf	Inf	missing	missing	unknown
297	3	false	0	false	true	meyer3	false	false	false	false	least_squares	unconstrained	-Inf	1.69361e9	true	missing	unknown
298	2	false	2	false	true	mgh01feas	true	false	false	false	other	general	-Inf	Inf	missing	missing	unknown
299	4	false	0	false	true	mgh09	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
300	3	false	0	false	true	mgh10	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
301	5	false	0	false	true	mgh17	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
302	2	false	0	false	true	misra1a	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
303	2	false	0	false	true	misra1b	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
304	2	false	0	false	true	misra1c	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
305	2	false	0	false	true	misra1d	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
306	100	true	0	false	true	morebv	false	false	false	false	least_squares	unconstrained	-Inf	0.500942	true	missing	unknown
307	2	false	0	false	true	nasty	false	false	false	false	other	unconstrained	-Inf	0.5	true	missing	unknown
308	100	true	0	false	true	ncb20	false	false	false	false	other	unconstrained	-Inf	182.002	true	missing	unknown
309	100	true	0	false	true	ncb20b	false	false	false	false	other	unconstrained	-Inf	200.0	true	missing	unknown
310	3	false	0	false	true	nelson	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
311	100	true	0	false	true	noncvxu2	false	false	false	false	other	unconstrained	-Inf	2.63975e6	true	missing	unknown
312	100	true	0	false	true	noncvxun	false	false	false	false	other	unconstrained	-Inf	2.72701e6	true	missing	unknown
313	100	true	0	false	true	nondia	false	false	false	false	other	unconstrained	-Inf	39604.0	true	missing	unknown
314	100	true	0	false	true	nondquar	false	false	false	false	other	unconstrained	-Inf	106.0	true	missing	unknown
315	5	false	0	false	true	osborne1	false	false	false	false	least_squares	unconstrained	-Inf	7.06876	true	missing	unknown
316	11	false	0	false	true	osborne2	false	false	false	false	least_squares	unconstrained	-Inf	2.09342	true	missing	unknown
317	8	false	0	false	true	palmer1c	false	false	false	false	least_squares	unconstrained	-Inf	3.45295e8	true	missing	unknown
318	7	false	0	false	true	palmer1d	false	false	false	false	least_squares	unconstrained	-Inf	2.87266e7	true	missing	unknown
319	8	false	0	false	true	palmer2c	false	false	false	false	least_squares	unconstrained	-Inf	2.6894e7	true	missing	unknown
320	8	false	0	false	true	palmer3c	false	false	false	false	least_squares	unconstrained	-Inf	8.12197e6	true	missing	unknown
321	8	false	0	false	true	palmer4c	false	false	false	false	least_squares	unconstrained	-Inf	8.09445e6	true	missing	unknown
322	6	false	0	false	true	palmer5c	false	false	false	false	least_squares	unconstrained	-Inf	25495.0	true	missing	unknown
323	4	false	0	false	true	palmer5d	false	false	false	false	least_squares	unconstrained	-Inf	22262.6	true	missing	unknown
324	8	false	0	false	true	palmer6c	false	false	false	false	least_squares	unconstrained	-Inf	7.72166e5	true	missing	unknown
325	8	false	0	false	true	palmer7c	false	false	false	false	least_squares	unconstrained	-Inf	3.20513e6	true	missing	unknown
326	8	false	0	false	true	palmer8c	false	false	false	false	least_squares	unconstrained	-Inf	850271.0	true	missing	unknown
327	100	true	0	false	true	penalty1	false	false	false	false	least_squares	unconstrained	-Inf	1.0	true	missing	unknown
328	100	true	0	false	true	penalty2	false	false	false	false	other	unconstrained	-Inf	1.68848e6	true	missing	unknown
329	100	true	0	false	true	penalty3	false	false	false	false	other	unconstrained	-Inf	1.00639e8	true	missing	unknown
330	100	true	50	true	true	polygon	false	false	true	false	other	linear	-Inf	Inf	false	missing	unknown
331	100	true	50	true	true	polygon1	false	false	true	false	other	linear	-Inf	Inf	false	missing	unknown
332	100	true	1	false	true	polygon2	true	false	true	false	other	linear	-Inf	Inf	false	missing	unknown
333	100	true	100	true	true	polygon3	false	true	false	false	other	general	-Inf	-0.0	true	missing	unknown
334	2	false	0	false	true	powellbs	false	false	false	false	other	unconstrained	-Inf	0.567631	true	missing	unknown
335	100	true	0	false	true	powellsg	false	false	false	false	other	unconstrained	-Inf	5375.0	true	missing	unknown
336	100	true	0	false	true	power	false	false	false	false	least_squares	unconstrained	-Inf	2.55025e7	true	missing	unknown
337	100	true	0	false	true	quartc	false	false	false	false	other	unconstrained	-Inf	1.85427e9	true	missing	unknown
338	3	false	0	false	true	rat42	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
339	4	false	0	false	true	rat43	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
340	109	true	102	true	true	robotarm	false	false	true	true	other	general	-Inf	Inf	missing	missing	unknown
341	2	false	0	false	true	rosenbrock	false	false	false	false	other	unconstrained	-Inf	32.3086	true	missing	unknown
342	4	false	0	false	true	rozman1	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
343	100	true	0	false	true	sbrybnd	false	false	false	false	least_squares	unconstrained	-Inf	1568.0	true	missing	unknown
344	100	true	0	false	true	schmvett	false	false	false	false	other	unconstrained	-Inf	-189.068	true	missing	unknown
345	100	true	0	false	true	scosine	false	false	false	false	other	unconstrained	-Inf	86.8807	true	missing	unknown
346	100	true	0	false	true	sinquad	false	false	false	false	other	unconstrained	-Inf	0.6561	true	missing	unknown
347	100	true	0	false	true	sparsine	false	false	false	false	other	unconstrained	-Inf	20893.3	true	missing	unknown
348	100	true	0	false	true	sparsqur	false	false	false	false	other	unconstrained	-Inf	1420.31	true	missing	unknown
349	100	true	0	false	true	spmsrtls	false	false	false	false	least_squares	unconstrained	-Inf	49.3239	true	missing	unknown
350	100	true	0	false	true	srosenbr	false	false	false	false	other	unconstrained	-Inf	1210.0	true	missing	unknown
351	600	true	44	true	true	structural	false	false	true	false	other	linear	-Inf	Inf	missing	missing	unknown
352	15	false	4	false	true	tetra	false	true	true	true	other	general	-Inf	Inf	missing	missing	unknown
353	12597	false	19222	false	true	tetra_duct12	false	true	true	true	other	general	-Inf	23246.1	true	missing	unknown
354	6417	false	9000	false	true	tetra_duct15	false	true	true	true	other	general	-Inf	10890.9	true	missing	unknown
355	3201	false	4104	false	true	tetra_duct20	false	true	true	true	other	general	-Inf	4959.8	true	missing	unknown
356	4011	false	4847	false	true	tetra_foam5	false	true	true	true	other	general	-Inf	6497.1	true	missing	unknown
357	2598	false	3116	false	true	tetra_gear	false	true	true	true	other	general	-Inf	4256.38	true	missing	unknown
358	3570	false	4675	false	true	tetra_hook	false	true	true	true	other	general	-Inf	6157.14	true	missing	unknown
359	30	false	0	false	true	threepk	false	false	true	false	other	unconstrained	-Inf	20236.5	true	missing	unknown
360	7	false	0	false	true	thurber	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
361	100	true	0	false	true	tointgss	false	false	false	false	other	unconstrained	-Inf	891.608	true	missing	unknown
362	100	true	0	false	true	tquartic	false	false	false	false	least_squares	unconstrained	-Inf	0.81	true	missing	unknown
363	8	false	3	false	true	triangle	false	true	true	true	other	general	-Inf	11.328	true	missing	unknown
364	2244	false	1896	false	true	triangle_deer	false	true	true	true	other	general	-Inf	2014.34	true	missing	unknown
365	1366	false	1182	false	true	triangle_pacman	false	true	true	true	other	general	-Inf	1316.28	true	missing	unknown
366	4444	false	4025	false	true	triangle_turtle	false	true	true	true	other	general	-Inf	4467.58	true	missing	unknown
367	100	true	0	false	true	tridia	false	false	false	false	other	unconstrained	-Inf	5049.0	true	missing	unknown
368	100	true	0	false	true	vardim	false	false	false	false	other	unconstrained	-Inf	1.31058e14	true	missing	unknown
369	8	false	0	false	true	vibrbeam	false	false	false	false	least_squares	unconstrained	-Inf	8231.28	true	missing	unknown
370	31	false	0	false	true	watson	false	false	false	false	least_squares	unconstrained	-Inf	500.0	true	missing	unknown
371	100	true	0	false	true	woods	false	false	false	false	other	unconstrained	-Inf	180451.0	true	missing	unknown
372	3	false	3	false	true	zangwil3	true	false	false	false	other	linear	-Inf	Inf	missing	missing	unknown

We select the problems that are scalable, so that there size can be modified. By default, the size is close to 100.

scalable_problems = meta[(meta.variable_nvar .== true) .& (meta.ncon .> 0), :name]

15-element Vector{String}:
 "camshape"
 "catenary"
 "chain"
 "channel"
 "clnlbeam"
 "controlinvestment"
 "elec"
 "hovercraft1d"
 "marine"
 "polygon"
 "polygon1"
 "polygon2"
 "polygon3"
 "robotarm"
 "structural"

using NLPModelsJuMP
list_backends = Dict(
  :forward => ADNLPModels.ForwardDiffADGradient,
  :reverse => ADNLPModels.ReverseDiffADGradient,
)

Dict{Symbol, DataType} with 2 entries:
  :reverse => ReverseDiffADGradient
  :forward => ForwardDiffADGradient

using DataFrames
nprob = length(scalable_problems)
stats = Dict{Symbol, DataFrame}()
for back in union(keys(list_backends), [:jump])
  stats[back] = DataFrame("name" => scalable_problems,
                 "time" => zeros(nprob),
                 "allocs" => zeros(Int, nprob))
end

using BenchmarkTools
nscal = 1000
for name in scalable_problems
  n = eval(Meta.parse("OptimizationProblems.get_" * name * "_nvar(n = $(nscal))"))
  m = eval(Meta.parse("OptimizationProblems.get_" * name * "_ncon(n = $(nscal))"))
  @info " $(name) with $n vars and $m cons"
  global x = ones(n)
  global g = zeros(n)
  global pb = Meta.parse(name)
  global nlp = MathOptNLPModel(OptimizationProblems.PureJuMP.eval(pb)(n = nscal))
  b = @benchmark grad!(nlp, x, g)
  stats[:jump][stats[:jump].name .== name, :time] = [median(b.times)]
  stats[:jump][stats[:jump].name .== name, :allocs] = [median(b.allocs)]
  for back in keys(list_backends)
    nlp = OptimizationProblems.ADNLPProblems.eval(pb)(n = nscal, gradient_backend = list_backends[back], matrix_free = true)
    b = @benchmark grad!(nlp, x, g)
    stats[back][stats[back].name .== name, :time] = [median(b.times)]
    stats[back][stats[back].name .== name, :allocs] = [median(b.allocs)]
  end
end

[ Info:  camshape with 1000 vars and 2003 cons
[ Info:  catenary with 999 vars and 332 cons
┌ Warning: catenary: number of variables adjusted to be a multiple of 3
└ @ OptimizationProblems.PureJuMP ~/.julia/packages/OptimizationProblems/9qr9C/src/PureJuMP/catenary.jl:20
┌ Warning: catenary: number of variables adjusted to be greater or equal to 6
└ @ OptimizationProblems.PureJuMP ~/.julia/packages/OptimizationProblems/9qr9C/src/PureJuMP/catenary.jl:22
┌ Warning: catenary: number of variables adjusted to be a multiple of 3
└ @ OptimizationProblems.ADNLPProblems ~/.julia/packages/OptimizationProblems/9qr9C/src/ADNLPProblems/catenary.jl:4
┌ Warning: catenary: number of variables adjusted to be greater or equal to 6
└ @ OptimizationProblems.ADNLPProblems ~/.julia/packages/OptimizationProblems/9qr9C/src/ADNLPProblems/catenary.jl:6
┌ Warning: catenary: number of variables adjusted to be a multiple of 3
└ @ OptimizationProblems.ADNLPProblems ~/.julia/packages/OptimizationProblems/9qr9C/src/ADNLPProblems/catenary.jl:4
┌ Warning: catenary: number of variables adjusted to be greater or equal to 6
└ @ OptimizationProblems.ADNLPProblems ~/.julia/packages/OptimizationProblems/9qr9C/src/ADNLPProblems/catenary.jl:6
[ Info:  chain with 1000 vars and 752 cons
[ Info:  channel with 1000 vars and 1000 cons
[ Info:  clnlbeam with 999 vars and 664 cons
[ Info:  controlinvestment with 1000 vars and 500 cons
[ Info:  elec with 999 vars and 333 cons
[ Info:  hovercraft1d with 998 vars and 668 cons
[ Info:  marine with 1007 vars and 488 cons
[ Info:  polygon with 1000 vars and 125251 cons
[ Info:  polygon1 with 1000 vars and 500 cons
[ Info:  polygon2 with 1000 vars and 1 cons
[ Info:  polygon3 with 1000 vars and 1000 cons
[ Info:  robotarm with 1009 vars and 1002 cons
[ Info:  structural with 3540 vars and 3652 cons

using Plots, SolverBenchmark
costnames = ["median time (in ns)", "median allocs"]
costs = [
  df -> df.time,
  df -> df.allocs,
]

gr()

profile_solvers(stats, costs, costnames)