With a JSO-compliant solver, such as CaNNOLeS, we can run the solver on a set of problems, explore the results, and compare to other JSO-compliant solvers using specialized benchmark tools. We are following here the tutorial in SolverBenchmark.jl to run benchmarks on JSO-compliant solvers.

using NLSProblems, NLPModels

To test the implementation of CaNNOLeS, we use the package NLSProblems.jl, which implements NLSProblemsModel an instance of AbstractNLPModel.

using SolverBenchmark

Let us select equality-constrained problems from NLSProblems with a maximum of 10000 variables or constraints. After removing problems with fixed variables, examples with a constant objective, and infeasibility residuals, we are left with 82 problems.

problems = (NLSProblems.eval(problem)() for problem in filter(x -> x != :NLSProblems, names(NLSProblems)) )
Base.Generator{Vector{Symbol}, Main.var"ex-ex1".var"#1#3"}(Main.var"ex-ex1".var"#1#3"(), [:BNST2, :BNST3, :LVcon501, :LVcon502, :LVcon503, :LVcon504, :LVcon511, :LVcon512, :LVcon513, :LVcon514  …  :tp354, :tp355, :tp358, :tp370, :tp371, :tp372, :tp373, :tp379, :tp394, :tp395])

We compare here CaNNOLeS with tron (Chih-Jen Lin and Jorge J. Moré, Newton's Method for Large Bound-Constrained Optimization Problems, SIAM J. Optim., 9(4), 1100–1127, 1999.), and trunk (A. R. Conn, N. I. M. Gould, and Ph. L. Toint (2000). Trust-Region Methods, volume 1 of MPS/SIAM Series on Optimization.) implemented in JSOSolvers.jl on a subset of NLSProblems problems.

using CaNNOLeS, JSOSolvers

To make stopping conditions comparable, we set tron's and trunk's parameters atol=0.0, and rtol=1e-5.

#Same time limit for all the solvers
max_time = 1200. #20 minutes

solvers = Dict(
  :tron => nlp -> tron(
    atol = 0.0,
    rtol = 1e-5,
  :trunk => nlp -> trunk(
    atol = 0.0,
    rtol = 1e-5,
  :cannoles => nlp -> cannoles(
    atol = 0.0,
    rtol = 1e-5,

stats = bmark_solvers(solvers, problems, skipif = nls -> !NLPModels.unconstrained(nls))
Dict{Symbol, DataFrames.DataFrame} with 3 entries:
  :tron     => 88×40 DataFrame…
  :trunk    => 88×40 DataFrame…
  :cannoles => 88×44 DataFrame…

The function bmark_solvers return a Dict of DataFrames with detailed information on the execution. This output can be saved in a data file.

using JLD2
@save "trunk_cannoles_$(string(length(problems))).jld2" stats

The result of the benchmark can be explored via tables,


or it can also be used to make performance profiles.

using Plots

legend = Dict(
  :neval_obj => "number of f evals",
  :neval_residual => "number of F evals",
  :neval_cons => "number of c evals",
  :neval_grad => "number of ∇f evals",
  :neval_jac => "number of ∇c evals",
  :neval_jprod => "number of ∇c*v evals",
  :neval_jtprod  => "number of ∇cᵀ*v evals",
  :neval_hess  => "number of ∇²f evals",
  :elapsed_time => "elapsed time"
perf_title(col) = "Performance profile on NLSProblems w.r.t. $(string(legend[col]))"

styles = [:solid, :dash, :dot, :dashdot]

function print_pp_column(col::Symbol, stats)

  ϵ = minimum(minimum(filter(x -> x > 0, df[!, col])) for df in values(stats))
  first_order(df) = df.status .== :first_order
  unbounded(df) = df.status .== :unbounded
  solved(df) = first_order(df) .| unbounded(df)
  cost(df) = (max.(df[!, col], ϵ) + .!solved(df) .* Inf)

  p = performance_profile(

print_pp_column(:elapsed_time, stats) # with respect to time
print_pp_column(:neval_residual, stats) # with respect to number of residual function evaluations