example.jl

using NLPModelsJuMP, JSOSolvers, JuMP

function example()
  model = Model()

  N = 10

  # Fake solution
  β_opt = [1.0; 2.0]

  # Fake data
  x = rand(N)
  y = rand(N)
  C = rand(N)
  z = rand(N)
  R = [(C[i] - β_opt[1] * z[i]) / ( (C[i] - β_opt[1] * z[i])^2 * (β_opt[2] - 1) + 1) for i = 1:N]
  data = β_opt[1] * x + R .* y + 0.01 * randn(N)

  β0 = [20.0; 10.0]
  @variable(model, β[i=1:2] ≥ 1, start=β0[i])

  @NLexpression(model, F[i=1:N], data[i] - β[1] * x[i] - y[i] * (C[i] - β[1] * z[i]) / ( (C[i] - β[1] * z[i])^2 * (β[2] - 1) + 1))

  nls = MathProgNLSModel(model, F)

  output = tron(nls, max_eval=10_000)
  println(output)
end

nls = example()

Project.toml

[deps]
JSOSolvers = "10dff2fc-5484-5881-a0e0-c90441020f8a"
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
NLPModelsJuMP = "792afdf1-32c1-5681-94e0-d7bf7a5df49e"

[compat]
JSOSolvers = "0.2.0"
JuMP = "0.18"
NLPModelsJuMP = "0.5.0"