Add least-squares in objective for detected NLS problems

[tmigot]

@paraynaud Extending the script to detect the NLS problems described in JuliaSmoothOptimizers/ExpressionTreeForge.jl#14

In this PR, the objective entry is updated in the Meta for the concerned problems. In a following PR, we will replace the ADNLPModel constructor by an ADNLSModel.

using ExpressionTreeForge
using ADNLPModels, ModelingToolkit
using OptimizationProblems, OptimizationProblems.ADNLPProblems

function get_expr_tree(adnlp :: ADNLPModel; x0 :: Vector{T}=copy(adnlp.meta.x0), kwargs...) where T <: Number
  n = adnlp.meta.nvar
  ModelingToolkit.@variables x[1:n]
  fun = adnlp.f(x)
  ex = ExpressionTreeForge.transform_to_expr_tree(fun)
  return ex, n, x0
end

using ..ExpressionTreeForge.M_power_operator

myand(a::Bool,b::Bool) = a && b

function isnls(nlp)
  ex, n, x0 = get_expr_tree(nlp)
  F_expr = delete_imbricated_plus(ex)
  test_square(expr) = expr.field == Power_operator{Int}(2)
  is_nls = mapreduce(test_square, myand, F_expr) :: Bool
  return is_nls 
end 

problems_names = OptimizationProblems.meta[!,:name] #261 problems
problems_symbols = map(name -> Symbol(name), problems_names)
problems = map( symbol -> getfield(OptimizationProblems.ADNLPProblems, symbol)(), problems_symbols)

res_isnls = []
index_is_nls = []
name_is_nls = []
for (index,problem) in enumerate(problems)
  println(index)
  try
    bool = isnls(problem)
    push!(res_isnls, bool)
    if bool
      push!(index_is_nls, index)
      push!(name_is_nls, problems_names[index])
    end
  catch 
    println("the ", index, "-th $(problems_names[index]) problem is unsupported")
  end 
end

length(res_isnls) #243 supported problems

global cpt_isnls = 0
for (index, is_nls) in enumerate(res_isnls)
  global cpt_isnls += is_nls
end 

name_is_nls # 45 NLS problems

for name in name_is_nls
  lines = readlines("src/Meta/$(name).jl")
  lines = map(line -> replace(line, ":objtype => :other," => ":objtype => :least_squares,"), lines)
  open("src/Meta/$(name).jl", "w") do io
    for line in lines
      println(io, line)
    end
  end
end

[paraynaud]

I got the same 45 problems, so it should be ok!

[codecov]

Codecov Report

Merging #199 (5d1f2bd) into main (66db451) will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##             main     #199   +/-   ##
=======================================
  Coverage   99.89%   99.89%           
=======================================
  Files         745      745           
  Lines        6639     6639           
=======================================
  Hits         6632     6632           
  Misses          7        7           

Impacted Files	Coverage Δ
src/Meta/arglina.jl	100.00% <ø> (ø)
src/Meta/arglinb.jl	100.00% <ø> (ø)
src/Meta/bdqrtic.jl	100.00% <ø> (ø)
src/Meta/beale.jl	100.00% <ø> (ø)
src/Meta/brownbs.jl	100.00% <ø> (ø)
src/Meta/brownden.jl	100.00% <ø> (ø)
src/Meta/brybnd.jl	100.00% <ø> (ø)
src/Meta/dixon3dq.jl	100.00% <ø> (ø)
src/Meta/errinros_mod.jl	100.00% <ø> (ø)
src/Meta/freuroth.jl	100.00% <ø> (ø)
... and 35 more

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[tmigot]

#162