CUTEst Quadratic Programming with Linear Constraints Benchmarks

Introduction

CUTEst, the Constraind and Unconstrained Testing Environment is, as the name suggests is a collection of around 1500 problems for general nonlinear optimization used to test optimization routines. The wrapper CUTEst.jl provides convenient access to the problem collection, which we can leverage to test the optimizers made available by Optimization.jl.

using Optimization
using OptimizationNLPModels
using CUTEst
using OptimizationOptimJL
using OptimizationOptimisers
using Ipopt
using OptimizationMOI
using OptimizationMOI: MOI as MOI
using DataFrames
using Plots
using StatsPlots
using StatsBase: countmap

optimizers = [
    ("Ipopt", MOI.OptimizerWithAttributes(Ipopt.Optimizer,
        "max_iter" => 5000,
        "tol" => 1e-6,
        "print_level" => 5)),
]

function get_stats(sol, optimizer_name)
    # Robustly get solve_time, even if stats or time is missing
    solve_time = try
        hasfield(typeof(sol), :stats) && hasfield(typeof(sol.stats), :time) ? getfield(sol.stats, :time) : NaN
    catch
        NaN
    end
    return (length(sol.u), solve_time, optimizer_name, Symbol(sol.retcode))
end

function run_benchmarks(problems, optimizers; chunk_size=1)
    problem = String[]
    n_vars = Int64[]
    secs = Float64[]
    solver = String[]
    retcode = Symbol[]
    optz = length(optimizers)
    n = length(problems)
    @info "Processing $(n) problems with $(optz) optimizers in chunks of $(chunk_size)"
    broadcast(c -> sizehint!(c, optz * n), [problem, n_vars, secs, solver, retcode])
    for chunk_start in 1:chunk_size:n
        chunk_end = min(chunk_start + chunk_size - 1, n)
        chunk_problems = problems[chunk_start:chunk_end]
        @info "Processing chunk $(div(chunk_start-1, chunk_size)+1)/$(div(n-1, chunk_size)+1): problems $(chunk_start)-$(chunk_end)"
        for (idx, prob_name) in enumerate(chunk_problems)
            current_problem = chunk_start + idx - 1
            @info "Problem $(current_problem)/$(n): $(prob_name)"
            nlp_prob = nothing
            try
                nlp_prob = CUTEstModel(prob_name)
                if nlp_prob.meta.nvar > 10000
                    @info "  Skipping $(prob_name) (too large: $(nlp_prob.meta.nvar) variables)"
                    finalize(nlp_prob)
                    continue
                end
                prob = OptimizationNLPModels.OptimizationProblem(nlp_prob, Optimization.AutoFiniteDiff())
                for (optimizer_name, optimizer) in optimizers
                    try
                        sol = solve(prob, optimizer; maxiters = 1000, maxtime = 30.0)
                        @info "✓ Solved $(prob_name) with $(optimizer_name) - Status: $(sol.retcode)"
                        vars, time, alg, code = get_stats(sol, optimizer_name)
                        push!(problem, prob_name)
                        push!(n_vars, vars)
                        push!(secs, time)
                        push!(solver, alg)
                        push!(retcode, code)
                    catch e
                        push!(problem, prob_name)
                        push!(n_vars, nlp_prob !== nothing ? nlp_prob.meta.nvar : -1)
                        push!(secs, NaN)
                        push!(solver, optimizer_name)
                        push!(retcode, :FAILED)
                    end
                end
            catch e
                for (optimizer_name, optimizer) in optimizers
                    push!(problem, prob_name)
                    push!(n_vars, -1)
                    push!(secs, NaN)
                    push!(solver, optimizer_name)
                    push!(retcode, :LOAD_FAILED)
                end
            finally
                if nlp_prob !== nothing
                    try
                        finalize(nlp_prob)
                    catch e
                    end
                end
            end
        end
        GC.gc()
        @info "Completed chunk, memory usage cleaned up"
    end
    return DataFrame(problem = problem, n_vars = n_vars, secs = secs, solver = solver, retcode = retcode)
end

run_benchmarks (generic function with 1 method)


# Benchmarks

We will be testing the [Ipopt]() and the [LBFGS]() optimizers on these classes of
problems.


# Quadratic programs with linear constraints

Lastly, we examine the problems with a quadratic objective function and only linear
constraints. There are 252 such problems in the suite.

julia

Select a moderate subset of quadratic problems for a realistic mix of successes and failures

quadproblems = CUTEst.selectsifproblems(objtype="quadratic", contype="linear") @info "Testing $(Expr(:incomplete, Base.Meta.ParseError("ParseError:\n# Error @ none:1:13\n(length(quad\n# └ ── Expected `)` or `,`", Base.JuliaSyntax.ParseError(Base.JuliaSyntax.SourceFile("(length(quad", 0, "none", 1, [1, 13]), Base.JuliaSyntax.Diagnostic[Base.JuliaSyntax.Diagnostic(13, 12, :error, "Expected `)` or `,`"), Base.JuliaSyntax.Diagnostic(13, 12, :error, "Expected `)` or `,`")], :other))))problems)) quadratic problems with linear constraints" quadproblems = quadproblems[1:min(30, length(quad_problems))]

Skip HIER13, BLOWEYA, LUKVLE8, PATTERNNE, READING2, NINENEW, READING6, DITTERT, CVXQP2, and MSS1 if present

quadproblems = filter(p -> !(lowercase(p) in ["hier13", "bloweya", "s268", "stcqp1", "cvxqp3", "avgasb", "lukvle8", "sosqp2", "patternne", "reading2", "ninenew", "reading6", "dittert", "liswet9", "cleuven4", "cvxqp2", "mss1", "mpc2", "cmpc10", "cmpc3"]), quadproblems) @info "Testing length(quad_problems) quadratic problems with linear constraints (subset)"

Harmonized analysis block with robust error handling and chunked processing

function runquadraticbenchmarks(problems, optimizers; chunksize=3) problem = String[] nvars = Int64[] secs = Float64[] solver = String[] retcode = Symbol[] optz = length(optimizers) n = length(problems) @info "Processing $(n) quadratic problems with $(optz) optimizers in chunks of $(chunk_size)" broadcast(c -> sizehint!(c, optz * n), [problem, n_vars, secs, solver, retcode]) for chunk_start in 1:chunk_size:n chunk_end = min(chunk_start + chunk_size - 1, n) chunk_problems = problems[chunk_start:chunk_end] @info "Processing chunk $(div(chunk_start-1, chunk_size)+1)/$(div(n-1, chunksize)+1): problems $(Expr(:incomplete, Base.Meta.ParseError("ParseError:\n# Error @ none:1:7\n(chunk\n# └ ── Expected `)` or `,`", Base.JuliaSyntax.ParseError(Base.JuliaSyntax.SourceFile("(chunk", 0, "none", 1, [1, 7]), Base.JuliaSyntax.Diagnostic[Base.JuliaSyntax.Diagnostic(7, 6, :error, "Expected `)` or `,`")], :other))))start)-$(chunk_end)" for (idx, prob_name) in enumerate(chunk_problems) current_problem = chunk_start + idx - 1 @info "Problem $(current_problem)/$(n): prob_name" nlpprob = nothing try nlpprob = CUTEstModel(probname) if nlpprob.meta.nvar > 10000 @info " Skipping prob_name (too large: nlp_prob.meta.nvar variables)" finalize(nlpprob) continue end prob = OptimizationNLPModels.OptimizationProblem(nlpprob, Optimization.AutoFiniteDiff()) for (optimizername, optimizer) in optimizers try sol = solve(prob, optimizer; maxiters = 1000, maxtime = 30.0) @info "✓ Solved $(Expr(:incomplete, Base.Meta.ParseError("ParseError:\n# Error @ none:1:6\n(prob\n# └ ── Expected `)` or `,`", Base.JuliaSyntax.ParseError(Base.JuliaSyntax.SourceFile("(prob", 0, "none", 1, [1, 6]), Base.JuliaSyntax.Diagnostic[Base.JuliaSyntax.Diagnostic(6, 5, :error, "Expected `)` or `,`")], :other))))name) with optimizer_name - Status: sol.retcode" vars, time, alg, code = getstats(sol, optimizername) push!(problem, probname) push!(nvars, vars) push!(secs, time) push!(solver, alg) push!(retcode, code) catch e push!(problem, probname) push!(nvars, nlpprob !== nothing ? nlpprob.meta.nvar : -1) push!(secs, NaN) push!(solver, optimizername) push!(retcode, :FAILED) println("ERROR: ", e) println("Stacktrace:") for (i, frame) in enumerate(stacktrace(e)) println(" ", i, ": ", frame) end end end catch e for (optimizername, optimizer) in optimizers push!(problem, probname) push!(nvars, -1) push!(secs, NaN) push!(solver, optimizername) push!(retcode, :LOADFAILED) end println("LOAD ERROR: ", e) println("Stacktrace:") for (i, frame) in enumerate(stacktrace(e)) println(" ", i, ": ", frame) end finally if nlpprob !== nothing try finalize(nlpprob) catch e end end end end GC.gc() @info "Completed chunk, memory usage cleaned up" end return DataFrame(problem = problem, nvars = nvars, secs = secs, solver = solver, retcode = retcode) end

quadresults = runquadraticbenchmarks(quadproblems, optimizers; chunk_size=3)

Calculate and display success rates for quadratic problems

successfulcodes = [:Success, :MaxIters, :MaxTime, :FirstOrderOptimal] successfulresults = filter(row -> row.retcode in successfulcodes, quadresults) totalattempts = nrow(quadresults) successfulattempts = nrow(successfulresults) successrate = totalattempts > 0 ? round(successfulattempts / totalattempts * 100, digits=1) : 0

@info "QUADRATIC PROBLEMS SUCCESS RATE: $(success_rate)% ($(successfulattempts)/$(Expr(:incomplete, Base.Meta.ParseError("ParseError:\n# Error @ none:1:7\n(total\n# └ ── Expected `)` or `,`", Base.JuliaSyntax.ParseError(Base.JuliaSyntax.SourceFile("(total", 0, "none", 1, [1, 7]), Base.JuliaSyntax.Diagnostic[Base.JuliaSyntax.Diagnostic(7, 6, :error, "Expected `)` or `,`")], :other))))attempts))"

println("Full results table for quadratic problems:") display(quad_results)

totalattempts = nrow(quadresults) successfulcodes = [:Success, :MaxIters, :MaxTime, :FirstOrderOptimal] successfulresults = filter(row -> row.retcode in successfulcodes, quadresults) successfulattempts = nrow(successfulresults) successrate = totalattempts > 0 ? round(successfulattempts / totalattempts * 100, digits=1) : 0

println("SUCCESS RATE ANALYSIS (Quadratic Problems):") println("Total attempts: ", totalattempts) println("Successful attempts: ", successfulattempts) println("Success rate: ", successrate, "%") println("Return code distribution:") if totalattempts > 0 for (code, count) in sort(collect(pairs(countmap(quad_results.retcode))), by=x->x[2], rev=true) println(" ", code, ": ", count, " occurrences") end else println(" No results to analyze") end

if nrow(quadresults) > 0 @df quadresults scatter(:nvars, :secs, group = :solver, xlabel = "n. variables", ylabel = "secs.", title = "Time to solution by optimizer and number of vars", ) println("Plotted quadratic problem results.") else println("No quadratic problem results to plot. DataFrame is empty.") println("Attempted problems:") println(quadproblems) end

This program contains Ipopt, a library for large-scale nonlinear optimizati on. Ipopt is released as open source code under the Eclipse Public License (EP L). For more information visit https://github.com/coin-or/Ipopt *************************************************************************** ***

This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 0 Number of nonzeros in inequality constraint Jacobian.: 2070 Number of nonzeros in Lagrangian Hessian.............: 26565

Total number of variables............................: 230 variables with only lower bounds: 215 variables with lower and upper bounds: 0 variables with only upper bounds: 0 Total number of equality constraints.................: 0 Total number of inequality constraints...............: 9 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 9

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 6.9998860e-04 2.14e+03 2.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 1.6683174e-03 2.13e+03 9.90e+03 -1.0 2.63e+00 6.0 6.28e-03 3.76e-0 3h 1 2 1.6998513e-03 2.13e+03 2.67e+04 -1.0 2.67e+00 8.2 1.00e-02 4.29e-0 5h 1 3r 1.6998513e-03 2.13e+03 9.99e+02 2.0 0.00e+00 8.7 0.00e+00 4.57e-0 7R 2 4r 7.1438721e-03 2.10e+03 9.98e+02 2.0 2.48e+04 - 4.37e-03 5.44e-0 5f 1 5r 3.6811146e-02 2.10e+03 9.95e+02 2.0 5.77e+01 2.0 1.05e-03 4.11e-0 3f 1 6r 3.6893306e-02 2.10e+03 1.11e+06 2.0 1.23e-01 6.9 9.91e-01 2.38e-0 1f 3 7r 3.6880816e-02 2.10e+03 4.49e+04 2.0 2.79e-05 9.2 9.94e-01 1.00e+0 0f 1 8r 3.6880329e-02 2.10e+03 7.37e+03 1.3 1.87e-06 9.6 1.00e+00 1.00e+0 0f 1 9r 3.6878928e-02 2.10e+03 7.40e+03 1.3 5.53e-06 9.1 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 10r 3.6875137e-02 2.10e+03 7.56e+03 1.3 1.74e-05 8.6 1.00e+00 1.00e+0 0f 1 11r 3.6873139e-02 2.10e+03 7.44e+03 1.3 6.33e-06 9.1 1.00e+00 1.00e+0 0f 1 12r 3.6868051e-02 2.10e+03 6.95e+03 1.3 1.76e-05 8.6 1.00e+00 1.00e+0 0f 1 13r 3.6866379e-02 2.10e+03 6.88e+03 1.3 6.64e-06 9.0 1.00e+00 1.00e+0 0f 1 14r 3.6855158e-02 2.10e+03 7.82e+03 1.3 2.06e-05 8.5 1.00e+00 1.00e+0 0f 1 15r 3.6852651e-02 2.10e+03 7.09e+03 1.3 7.59e-06 9.0 1.00e+00 1.00e+0 0f 1 16r 3.6841171e-02 2.10e+03 7.51e+03 1.3 2.36e-05 8.5 1.00e+00 1.00e+0 0f 1 17r 3.6838632e-02 2.10e+03 6.65e+03 1.3 7.95e-06 8.9 1.00e+00 1.00e+0 0f 1 18r 3.6824962e-02 2.10e+03 8.81e+03 1.3 2.28e-05 8.4 1.00e+00 1.00e+0 0f 1 19r 3.6821939e-02 2.10e+03 6.58e+03 1.3 8.82e-06 8.9 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 20r 3.6820848e-02 2.10e+03 6.49e+03 1.3 3.27e-06 9.3 1.00e+00 1.00e+0 0f 1 21r 3.6817952e-02 2.10e+03 6.21e+03 1.3 9.57e-06 8.8 1.00e+00 1.00e+0 0f 1 22r 3.6816829e-02 2.10e+03 6.36e+03 1.3 3.66e-06 9.2 1.00e+00 1.00e+0 0f 1 23r 3.6812495e-02 2.10e+03 6.51e+03 1.3 1.10e-05 8.8 1.00e+00 1.00e+0 0f 1 24r 3.6778906e-02 2.10e+03 8.83e+03 1.3 4.47e-05 8.3 1.00e+00 1.00e+0 0f 1 25r 3.6772810e-02 2.10e+03 6.62e+03 1.3 1.22e-05 8.7 1.00e+00 1.00e+0 0f 1 26r 3.6771355e-02 2.10e+03 5.89e+03 1.3 4.14e-06 9.1 1.00e+00 1.00e+0 0f 1 27r 3.6764939e-02 2.10e+03 6.18e+03 1.3 1.32e-05 8.7 1.00e+00 1.00e+0 0f 1 28r 3.6763312e-02 2.10e+03 5.63e+03 1.3 4.64e-06 9.1 1.00e+00 1.00e+0 0f 1 29r 3.6758784e-02 2.10e+03 5.42e+03 1.3 1.35e-05 8.6 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 30r 3.6756824e-02 2.10e+03 5.74e+03 1.3 5.17e-06 9.0 1.00e+00 1.00e+0 0f 1 31r 3.6752687e-02 2.10e+03 5.50e+03 1.3 1.56e-05 8.6 1.00e+00 1.00e+0 0f 1

Number of Iterations....: 31

                               (scaled)                 (unscaled)

Objective...............: 3.6752687389453066e-02 3.6752687389453066e-0 2 Dual infeasibility......: 5.4998814584083348e+03 5.4998814584083348e+0 3 Constraint violation....: 1.0358170696823382e+02 2.0985653831764175e+0 3 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 2.1000219021273175e+01 2.1000219021273175e+0 1 Overall NLP error.......: 2.0491729862306448e+02 5.4998814584083348e+0 3

Number of objective function evaluations = 39 Number of objective gradient evaluations = 5 Number of equality constraint evaluations = 0 Number of inequality constraint evaluations = 39 Number of equality constraint Jacobian evaluations = 0 Number of inequality constraint Jacobian evaluations = 33 Number of Lagrangian Hessian evaluations = 31 Total seconds in IPOPT = 30.272

EXIT: Maximum wallclock time exceeded. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 3456 Number of nonzeros in inequality constraint Jacobian.: 131328 Number of nonzeros in Lagrangian Hessian.............: 73920

Total number of variables............................: 384 variables with only lower bounds: 228 variables with lower and upper bounds: 156 variables with only upper bounds: 0 Total number of equality constraints.................: 9 Total number of inequality constraints...............: 342 inequality constraints with only lower bounds: 249 inequality constraints with lower and upper bounds: 89 inequality constraints with only upper bounds: 4

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 1.2095848e+01 2.66e+03 2.73e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 1.2112651e+01 2.66e+03 3.81e+04 -1.0 8.32e+02 6.0 2.41e-05 4.58e-0 5h 1 2r 1.2112651e+01 2.66e+03 9.99e+02 3.4 0.00e+00 10.0 0.00e+00 2.30e-0 7R 2 3r 1.3517874e+01 2.66e+03 9.99e+02 3.4 1.45e+05 - 1.35e-05 1.70e-0 5f 1 4r 1.3516741e+01 2.66e+03 1.76e+05 1.3 1.09e-01 6.0 9.82e-01 6.02e-0 2f 2 5r 1.3516877e+01 2.66e+03 9.75e+03 1.3 4.65e-04 7.3 1.00e+00 1.00e+0 0f 1

Number of Iterations....: 5

                               (scaled)                 (unscaled)

Objective...............: 1.3516877060346227e+01 1.3516877060346227e+0 1 Dual infeasibility......: 9.7543137332571878e+03 9.7543137332571878e+0 3 Constraint violation....: 2.6558523048824864e+03 2.6558523048824864e+0 3 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 4.0344181589675742e+01 4.0344181589675742e+0 1 Overall NLP error.......: 2.6558523048824864e+03 9.7543137332571878e+0 3

Number of objective function evaluations = 11 Number of objective gradient evaluations = 4 Number of equality constraint evaluations = 11 Number of inequality constraint evaluations = 11 Number of equality constraint Jacobian evaluations = 7 Number of inequality constraint Jacobian evaluations = 7 Number of Lagrangian Hessian evaluations = 5 Total seconds in IPOPT = 30.186

EXIT: Maximum wallclock time exceeded. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 96 Number of nonzeros in inequality constraint Jacobian.: 0 Number of nonzeros in Lagrangian Hessian.............: 4656

Total number of variables............................: 96 variables with only lower bounds: 0 variables with lower and upper bounds: 96 variables with only upper bounds: 0 Total number of equality constraints.................: 1 Total number of inequality constraints...............: 0 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 0

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 4.1972504e-01 4.00e-02 4.77e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 9.6266670e-02 1.79e-15 3.49e-02 -1.0 1.46e-02 - 1.00e+00 1.00e+0 0h 1 2 8.5167968e-02 3.19e-16 7.55e-01 -2.5 2.36e-03 - 9.21e-01 1.00e+0 0f 1 3 5.7281281e-02 3.64e-17 7.13e-03 -2.5 1.20e-02 - 1.00e+00 1.00e+0 0f 1 4 4.1007753e-02 4.48e-16 1.17e-01 -3.8 6.45e-03 - 7.94e-01 1.00e+0 0f 1 5 3.5972456e-02 1.18e-16 6.24e-02 -3.8 4.94e-03 - 7.55e-01 1.00e+0 0f 1 6 3.4734557e-02 3.47e-18 4.76e-03 -3.8 2.51e-03 - 1.00e+00 1.00e+0 0f 1 7 3.4469655e-02 4.68e-17 1.56e-03 -3.8 5.21e-04 - 1.00e+00 1.00e+0 0f 1 8 3.4463910e-02 2.98e-16 1.46e-04 -3.8 8.22e-05 - 1.00e+00 1.00e+0 0f 1 9 3.3925583e-02 2.93e-16 8.18e-03 -5.7 1.51e-03 - 9.04e-01 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 10 3.3789299e-02 6.56e-16 2.32e-03 -5.7 6.83e-04 - 1.00e+00 1.00e+0 0f 1 11 3.3744681e-02 7.63e-16 3.66e-03 -5.7 5.50e-04 - 1.00e+00 1.00e+0 0f 1 12 3.3741502e-02 1.06e-16 4.00e-04 -5.7 1.80e-04 - 1.00e+00 1.00e+0 0f 1 13 3.3741499e-02 1.39e-17 5.53e-05 -5.7 2.18e-05 - 1.00e+00 1.00e+0 0f 1 14 3.3741494e-02 2.62e-16 5.66e-06 -5.7 1.83e-06 - 1.00e+00 1.00e+0 0h 1 15 3.3734554e-02 6.77e-17 4.54e-04 -7.0 1.32e-04 - 1.00e+00 1.00e+0 0f 1 16 3.3734043e-02 1.42e-16 7.76e-05 -7.0 5.13e-05 - 1.00e+00 1.00e+0 0f 1 17 3.3734036e-02 3.89e-16 2.41e-05 -7.0 8.69e-06 - 1.00e+00 1.00e+0 0h 1 18 3.3734037e-02 2.50e-16 3.17e-06 -7.0 1.85e-06 - 1.00e+00 1.00e+0 0h 1 19 3.3734037e-02 3.05e-16 7.25e-07 -7.0 2.89e-07 - 1.00e+00 1.00e+0 0h 1

Number of Iterations....: 19

                               (scaled)                 (unscaled)

Objective...............: 3.3734036836557693e-02 3.3734036836557693e-0 2 Dual infeasibility......: 7.2498226292322491e-07 7.2498226292322491e-0 7 Constraint violation....: 3.0531133177191805e-16 3.0531133177191805e-1 6 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 9.0909090909090915e-08 9.0909090909090915e-0 8 Overall NLP error.......: 7.2498226292322491e-07 7.2498226292322491e-0 7

Number of objective function evaluations = 20 Number of objective gradient evaluations = 20 Number of equality constraint evaluations = 20 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 20 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 19 Total seconds in IPOPT = 17.471

EXIT: Optimal Solution Found. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 0 Number of nonzeros in inequality constraint Jacobian.: 3 Number of nonzeros in Lagrangian Hessian.............: 6

Total number of variables............................: 3 variables with only lower bounds: 3 variables with lower and upper bounds: 0 variables with only upper bounds: 0 Total number of equality constraints.................: 0 Total number of inequality constraints...............: 1 inequality constraints with only lower bounds: 1 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 0

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 2.2500000e+00 0.00e+00 2.71e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 7.9307609e-01 0.00e+00 2.71e+00 -1.0 1.12e+00 - 3.25e-01 8.25e-0 1f 1 2 6.6886239e-01 0.00e+00 4.69e+00 -1.0 4.68e-02 2.0 1.00e+00 1.00e+0 0f 1 3 4.1836368e-01 0.00e+00 8.14e-01 -1.0 2.04e-01 - 9.21e-01 1.00e+0 0f 1 4 3.7672986e-01 0.00e+00 9.02e-01 -1.7 3.10e-02 1.5 1.00e+00 1.00e+0 0f 1 5 2.1085739e-01 0.00e+00 3.76e-01 -1.7 2.17e-01 - 6.54e-01 1.00e+0 0f 1 6 1.6849109e-01 0.00e+00 2.85e-01 -1.7 3.97e-01 - 1.00e+00 3.89e-0 1f 2 7 1.6172448e-01 0.00e+00 2.16e-01 -1.7 2.07e-02 1.0 1.00e+00 1.00e+0 0f 1 8 1.3674336e-01 0.00e+00 2.42e-01 -1.7 1.74e+00 - 4.05e-01 7.67e-0 2f 2 9 1.2903102e-01 0.00e+00 4.50e-02 -1.7 6.69e-02 - 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 10 1.2316475e-01 0.00e+00 9.18e-02 -2.5 2.48e-02 0.6 1.00e+00 1.00e+0 0f 1 11 1.2059806e-01 0.00e+00 1.12e-01 -2.5 1.14e-02 1.0 1.00e+00 1.00e+0 0f 1 12 1.1639040e-01 0.00e+00 6.53e-02 -2.5 1.07e-01 - 1.00e+00 1.99e-0 1f 2 13 1.1442786e-01 0.00e+00 3.24e-02 -2.5 1.33e-02 - 1.00e+00 1.00e+0 0f 1 14 1.1397550e-01 0.00e+00 6.35e-03 -2.5 1.93e-03 0.5 1.00e+00 1.00e+0 0f 1 15 1.1119836e-01 0.00e+00 6.62e-03 -3.8 1.24e-02 - 1.00e+00 1.00e+0 0f 1 16 1.1126059e-01 0.00e+00 2.32e-04 -3.8 2.80e-04 - 1.00e+00 1.00e+0 0f 1 17 1.1111270e-01 0.00e+00 1.43e-03 -5.7 6.66e-04 - 1.00e+00 1.00e+0 0f 1 18 1.1111295e-01 0.00e+00 1.68e-04 -5.7 1.53e-04 - 1.00e+00 1.00e+0 0f 1 19 1.1111295e-01 0.00e+00 2.54e-05 -5.7 2.25e-05 - 1.00e+00 1.00e+0 0h 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 20 1.1111295e-01 0.00e+00 1.31e-05 -5.7 2.27e-06 - 1.00e+00 1.00e+0 0h 1 21 1.1111120e-01 0.00e+00 1.92e-05 -7.0 1.60e-05 0.0 1.00e+00 1.00e+0 0f 1 22 1.1111120e-01 0.00e+00 7.86e-06 -7.0 6.21e-06 - 1.00e+00 1.00e+0 0h 1 23 1.1111120e-01 0.00e+00 2.17e-06 -7.0 1.03e-06 0.5 1.00e+00 1.00e+0 0h 1 24 1.1111120e-01 0.00e+00 1.38e-06 -7.0 2.28e-06 - 1.00e+00 5.00e-0 1h 2 25 1.1111120e-01 0.00e+00 6.94e-07 -7.0 6.70e-08 0.9 1.00e+00 1.00e+0 0h 1

Number of Iterations....: 25

                               (scaled)                 (unscaled)

Objective...............: 1.1111119979804229e-01 1.1111119979804229e-0 1 Dual infeasibility......: 6.9435271937006593e-07 6.9435271937006593e-0 7 Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+0 0 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 9.0909090909092715e-08 9.0909090909092715e-0 8 Overall NLP error.......: 6.9435271937006593e-07 6.9435271937006593e-0 7

Number of objective function evaluations = 33 Number of objective gradient evaluations = 26 Number of equality constraint evaluations = 0 Number of inequality constraint evaluations = 33 Number of equality constraint Jacobian evaluations = 0 Number of inequality constraint Jacobian evaluations = 26 Number of Lagrangian Hessian evaluations = 25 Total seconds in IPOPT = 0.010

EXIT: Optimal Solution Found. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 0 Number of nonzeros in inequality constraint Jacobian.: 183750 Number of nonzeros in Lagrangian Hessian.............: 15400

Total number of variables............................: 175 variables with only lower bounds: 0 variables with lower and upper bounds: 0 variables with only upper bounds: 0 Total number of equality constraints.................: 0 Total number of inequality constraints...............: 1050 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 1050

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 0.0000000e+00 4.98e-02 9.92e-01 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 9.1177485e-02 4.91e-02 1.40e+02 -1.0 5.61e-02 4.0 1.00e+00 1.77e-0 1h 1 2 9.1714461e-02 4.90e-02 5.26e+03 -1.0 4.03e-02 4.4 1.00e+00 3.52e-0 3h 1 3 1.0187941e-01 4.66e-02 3.52e+04 -1.0 5.71e-02 4.9 1.00e+00 4.92e-0 2h 1

Number of Iterations....: 3

                               (scaled)                 (unscaled)

Objective...............: 1.0187940613798399e-01 1.0187940613798399e-0 1 Dual infeasibility......: 3.5188718182804369e+04 3.5188718182804369e+0 4 Constraint violation....: 4.6630028933483177e-02 4.6630028933483177e-0 2 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 2.3426454706504036e+00 2.3426454706504036e+0 0 Overall NLP error.......: 3.5188718182804369e+04 3.5188718182804369e+0 4

Number of objective function evaluations = 4 Number of objective gradient evaluations = 4 Number of equality constraint evaluations = 0 Number of inequality constraint evaluations = 4 Number of equality constraint Jacobian evaluations = 0 Number of inequality constraint Jacobian evaluations = 4 Number of Lagrangian Hessian evaluations = 3 Total seconds in IPOPT = 42.578

EXIT: Maximum wallclock time exceeded. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 3456 Number of nonzeros in inequality constraint Jacobian.: 131328 Number of nonzeros in Lagrangian Hessian.............: 73920

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 1.2057448e+01 2.66e+03 2.73e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 1.2070111e+01 2.66e+03 3.82e+04 -1.0 8.33e+02 6.0 2.41e-05 4.59e-0 5h 1 2r 1.2070111e+01 2.66e+03 9.99e+02 3.4 0.00e+00 10.9 0.00e+00 2.29e-0 7R 2 3r 1.3176285e+01 2.66e+03 9.99e+02 3.4 1.45e+05 - 1.34e-05 1.69e-0 5f 1 4r 1.3175686e+01 2.66e+03 1.76e+05 1.3 1.09e-01 6.0 9.82e-01 6.04e-0 2f 2 5r 1.3175805e+01 2.66e+03 1.00e+04 1.3 4.73e-04 7.3 1.00e+00 1.00e+0 0f 1

Number of Iterations....: 5

                               (scaled)                 (unscaled)

Objective...............: 1.3175805238032627e+01 1.3175805238032627e+0 1 Dual infeasibility......: 1.0038478290146477e+04 1.0038478290146477e+0 4 Constraint violation....: 2.6558526154466922e+03 2.6558526154466922e+0 3 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 3.9844453499617295e+01 3.9844453499617295e+0 1 Overall NLP error.......: 2.6558526154466922e+03 1.0038478290146477e+0 4

Number of objective function evaluations = 9 Number of objective gradient evaluations = 4 Number of equality constraint evaluations = 9 Number of inequality constraint evaluations = 9 Number of equality constraint Jacobian evaluations = 7 Number of inequality constraint Jacobian evaluations = 7 Number of Lagrangian Hessian evaluations = 5 Total seconds in IPOPT = 30.253

EXIT: Maximum wallclock time exceeded. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 91512 Number of nonzeros in inequality constraint Jacobian.: 0 Number of nonzeros in Lagrangian Hessian.............: 808356

Total number of variables............................: 1271 variables with only lower bounds: 0 variables with lower and upper bounds: 1271 variables with only upper bounds: 0 Total number of equality constraints.................: 72 Total number of inequality constraints...............: 0 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 0

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 1.8553735e+00 1.01e+01 2.12e-01 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 1.8742171e+00 7.55e+00 1.13e+01 -1.0 3.73e-01 2.0 9.90e-01 2.52e-0 1h 1

Number of Iterations....: 1

                               (scaled)                 (unscaled)

Objective...............: 1.8742171418847360e+00 1.8742171418847360e+0 0 Dual infeasibility......: 1.1340415586752636e+01 1.1340415586752636e+0 1 Constraint violation....: 7.5501556656700490e+00 7.5501556656700490e+0 0 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 2.0604460819772835e+03 2.0604460819772835e+0 3 Overall NLP error.......: 2.0604460819772835e+03 2.0604460819772835e+0 3

Number of objective function evaluations = 2 Number of objective gradient evaluations = 2 Number of equality constraint evaluations = 2 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 2 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 1 Total seconds in IPOPT = 68.725

EXIT: Maximum wallclock time exceeded. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 8 Number of nonzeros in inequality constraint Jacobian.: 2216 Number of nonzeros in Lagrangian Hessian.............: 36

Total number of variables............................: 8 variables with only lower bounds: 0 variables with lower and upper bounds: 8 variables with only upper bounds: 0 Total number of equality constraints.................: 1 Total number of inequality constraints...............: 277 inequality constraints with only lower bounds: 277 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 0

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 6.0067449e+01 9.20e-01 1.00e+02 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 7.3421159e+01 9.02e-01 9.88e+01 -1.0 1.01e+02 - 1.51e-02 1.94e-0 2f 1 2 7.3706124e+01 9.02e-01 3.00e+02 -1.0 1.28e+02 2.0 1.59e-02 9.00e-0 5h 1 3 8.4670525e+01 8.99e-01 8.78e+02 -1.0 1.18e+02 1.5 3.42e-02 3.44e-0 3h 1 4 8.4868270e+01 8.99e-01 5.27e+04 -1.0 1.25e+02 2.9 2.34e-02 5.00e-0 5h 1 5 9.3349073e+01 8.97e-01 8.04e+05 -1.0 1.39e+02 3.3 4.90e-02 1.73e-0 3h 1 6 9.5449773e+01 8.97e-01 2.76e+06 -1.0 1.21e+02 3.7 4.76e-02 6.47e-0 4h 1 7 9.8210283e+01 8.96e-01 1.46e+07 -1.0 1.10e+02 4.1 7.51e-02 9.81e-0 4h 1 8 1.5192091e+02 8.80e-01 4.02e+07 -1.0 9.75e+01 4.6 5.76e-02 1.76e-0 2h 1 9 1.5788682e+02 8.78e-01 1.76e+09 -1.0 9.45e+01 5.9 1.09e-01 2.26e-0 3h 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 10 2.2520920e+02 8.66e-01 2.42e+09 -1.0 1.60e+02 6.3 2.65e-02 1.40e-0 2h 1 11 2.3290562e+02 8.63e-01 8.68e+10 -1.0 8.66e+01 7.6 1.15e-01 2.78e-0 3h 1 12 2.3533260e+02 8.63e-01 9.85e+10 -1.0 1.84e+02 8.1 2.41e-02 3.80e-0 4h 1 13 2.6938433e+02 8.53e-01 7.63e+10 -1.0 8.63e+01 8.5 3.05e-04 1.16e-0 2h 1 14 2.7198683e+02 8.53e-01 2.27e+13 -1.0 8.71e+01 9.8 2.22e-01 6.61e-0 4h 1 15 5.5045656e+02 8.10e-01 1.89e+13 -1.0 9.51e+01 9.3 1.38e-03 5.01e-0 2h 1 16 5.5679191e+02 8.09e-01 1.67e+14 -1.0 8.56e+01 10.7 2.05e-01 1.19e-0 3h 1 17 4.5543200e+02 8.09e-01 1.46e+14 -1.0 3.95e+08 - 3.12e-13 3.38e-0 9f 1 18 6.3381611e+02 7.82e-01 1.87e+15 -1.0 8.51e+01 11.1 9.35e-01 3.32e-0 2h 1 19 6.5300468e+02 7.81e-01 2.44e+15 -1.0 2.40e+02 12.4 9.42e-03 1.91e-0 3h 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 20 6.5893001e+02 7.80e-01 1.49e+17 -1.0 8.04e+01 13.8 1.89e-01 1.19e-0 3h 1 21 6.5900191e+02 7.80e-01 1.21e+18 -1.0 8.09e+01 14.2 5.20e-01 1.21e-0 5h 1 22 1.4383138e+04 9.43e-17 4.26e+17 -1.0 7.80e+01 13.7 1.08e-07 1.00e+0 0h 1 23 1.4383138e+04 9.41e-17 1.21e+16 -1.0 5.24e-14 15.9 9.90e-01 1.00e+0 0 0 24 1.4383138e+04 1.90e-16 1.21e+14 -1.0 3.77e-14 15.5 9.90e-01 1.00e+0 0 0 25 1.4383138e+04 3.88e-17 1.21e+12 -1.0 1.10e-13 15.0 9.90e-01 1.00e+0 0f 1 26 1.4383138e+04 2.39e-17 1.21e+10 -1.0 1.23e-11 14.5 9.90e-01 1.00e+0 0f 1 27 1.4383138e+04 1.92e-16 1.03e+08 -1.0 1.23e-09 14.0 9.91e-01 1.00e+0 0f 1 28 1.4383138e+04 8.73e-17 3.61e+06 -1.0 1.01e-07 13.6 1.00e+00 1.00e+0 0f 1 29 1.4383138e+04 6.13e-17 1.90e+05 -1.0 1.59e-08 13.1 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 30 1.4383138e+04 1.62e-17 4.59e+05 -1.0 1.16e-07 12.6 1.00e+00 1.00e+0 0f 1 31 1.4383138e+04 1.44e-16 1.32e+05 -1.0 9.96e-08 12.1 1.00e+00 1.00e+0 0f 1 32 1.4383138e+04 9.50e-17 1.21e+05 -1.0 2.74e-07 11.6 1.00e+00 1.00e+0 0f 1 33 1.4383138e+04 1.51e-17 5.35e+04 -1.0 3.64e-07 11.2 1.00e+00 1.00e+0 0f 1 34 1.4383137e+04 3.53e-17 3.70e+04 -1.0 7.57e-07 10.7 1.00e+00 1.00e+0 0f 1 35 1.4383137e+04 1.18e-16 1.91e+04 -1.0 1.17e-06 10.2 1.00e+00 1.00e+0 0f 1 36 1.4383136e+04 1.08e-16 1.19e+04 -1.0 2.19e-06 9.7 1.00e+00 1.00e+0 0f 1 37 1.4383135e+04 7.05e-17 6.56e+03 -1.0 3.62e-06 9.3 1.00e+00 1.00e+0 0f 1 38 1.4383133e+04 7.43e-17 3.91e+03 -1.0 6.48e-06 8.8 1.00e+00 1.00e+0 0f 1 39 1.4383129e+04 9.97e-17 2.21e+03 -1.0 1.10e-05 8.3 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 40 1.4383122e+04 2.21e-16 1.30e+03 -1.0 1.93e-05 7.8 1.00e+00 1.00e+0 0f 1 41 1.4383110e+04 1.03e-16 7.44e+02 -1.0 3.32e-05 7.3 1.00e+00 1.00e+0 0f 1 42 1.4383089e+04 4.05e-17 4.33e+02 -1.0 5.81e-05 6.9 1.00e+00 1.00e+0 0f 1 43 1.4383051e+04 1.13e-17 2.50e+02 -1.0 1.01e-04 6.4 1.00e+00 1.00e+0 0f 1 44 1.4382981e+04 2.76e-17 1.46e+02 -1.0 1.76e-04 5.9 1.00e+00 1.00e+0 0f 1 45 1.4382849e+04 9.10e-17 8.54e+01 -1.0 3.09e-04 5.4 1.00e+00 1.00e+0 0f 1 46 1.4382584e+04 1.15e-16 5.06e+01 -1.0 5.50e-04 5.0 1.00e+00 1.00e+0 0f 1 47 1.4382020e+04 7.59e-17 3.05e+01 -1.0 9.93e-04 4.5 1.00e+00 1.00e+0 0f 1 48 1.4380721e+04 1.08e-16 1.92e+01 -1.0 1.87e-03 4.0 1.00e+00 1.00e+0 0f 1 49 1.4377497e+04 4.48e-17 1.44e+01 -1.0 4.22e-03 3.5 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 50 1.4368912e+04 6.72e-18 1.17e+01 -1.0 1.03e-02 3.1 1.00e+00 1.00e+0 0f 1 51 1.4344651e+04 1.10e-17 1.03e+01 -1.0 2.72e-02 2.6 1.00e+00 1.00e+0 0f 1 52 1.4273388e+04 6.08e-17 9.62e+00 -1.0 7.62e-02 2.1 1.00e+00 1.00e+0 0f 1 53 1.4064935e+04 1.88e-17 1.71e+01 -1.0 2.20e-01 1.6 8.65e-01 1.00e+0 0f 1 54 1.3458814e+04 9.63e-17 4.30e+01 -1.0 6.55e-01 1.1 1.00e+00 1.00e+0 0f 1 55 1.1896493e+04 1.89e-17 1.27e+02 -1.0 1.83e+00 0.7 4.50e-01 1.00e+0 0f 1 56 8.7653654e+03 2.03e-16 2.74e+02 -1.0 3.96e+00 0.2 7.40e-01 1.00e+0 0f 1 57 7.6313046e+03 9.39e-17 1.40e+02 -1.0 1.64e+00 0.6 1.00e+00 1.00e+0 0f 1 58 7.0602727e+03 2.27e-17 2.27e+02 -1.0 3.26e+00 0.1 1.00e+00 2.70e-0 1f 1 59 4.9745073e+03 3.04e-18 1.66e+02 -1.0 7.08e+00 -0.3 3.11e-01 5.57e-0 1f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 60 4.7045249e+03 5.94e-17 4.47e+02 -1.0 1.07e+01 -0.8 1.00e+00 5.92e-0 2f 1 61 2.4792342e+03 1.62e-16 2.21e+02 -1.0 7.16e+00 -0.4 1.00e+00 1.00e+0 0f 1 62 1.3530002e+03 4.68e-17 6.98e+02 -1.0 1.62e+01 -0.9 4.62e-02 1.00e+0 0f 1 63 8.5029316e+02 3.47e-18 1.07e+02 -1.0 4.65e+00 -0.4 1.00e+00 1.00e+0 0f 1 64 7.1699805e+02 9.02e-17 3.31e+01 -1.0 1.38e+00 -0.0 4.84e-01 1.00e+0 0f 1 65 6.7656107e+02 2.78e-17 3.60e+01 -1.0 2.25e+00 -0.5 7.25e-01 2.07e-0 1f 1 66 5.0995086e+02 1.25e-16 6.57e+01 -1.0 7.53e+00 - 3.88e-01 4.53e-0 1f 1 67 4.5284647e+02 1.11e-16 6.18e+01 -1.0 5.67e+00 -1.0 4.18e-01 2.65e-0 1f 1 68 4.4401718e+02 0.00e+00 5.31e+00 -1.0 1.58e+00 - 1.00e+00 1.00e+0 0f 1 69 4.3118372e+02 2.22e-16 6.59e-01 -1.0 4.37e-01 - 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 70 4.2832398e+02 2.78e-17 3.93e-01 -1.7 1.23e-01 - 1.00e+00 1.00e+0 0f 1 71 4.2816868e+02 8.33e-17 9.22e-02 -1.7 2.98e-02 - 1.00e+00 1.00e+0 0f 1 72 4.2738920e+02 0.00e+00 8.02e-02 -2.5 3.84e-02 - 1.00e+00 1.00e+0 0f 1 73 4.2736683e+02 5.55e-17 1.23e-02 -2.5 5.48e-03 - 1.00e+00 1.00e+0 0f 1 74 4.2724048e+02 1.39e-16 6.07e-03 -3.8 7.08e-03 - 1.00e+00 1.00e+0 0f 1 75 4.2723969e+02 5.55e-17 1.30e-03 -3.8 6.44e-04 - 1.00e+00 1.00e+0 0f 1 76 4.2723263e+02 0.00e+00 7.22e-04 -5.7 4.16e-04 - 1.00e+00 1.00e+0 0f 1 77 4.2723263e+02 1.94e-16 2.22e-05 -5.7 2.84e-05 - 1.00e+00 1.00e+0 0h 1 78 4.2723263e+02 1.11e-16 5.24e-06 -5.7 1.22e-06 - 1.00e+00 1.00e+0 0h 1 79 4.2723254e+02 1.11e-16 4.20e-06 -7.0 4.87e-06 - 1.00e+00 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 80 4.2723254e+02 8.33e-17 4.20e-07 -7.0 2.44e-07 - 1.00e+00 1.00e+0 0h 1

Number of Iterations....: 80

                               (scaled)                 (unscaled)

Objective...............: 2.6954156297485696e+01 4.2723254442370506e+0 2 Dual infeasibility......: 4.2045888000871561e-07 6.6644162462032336e-0 6 Constraint violation....: 8.3266726846886741e-17 8.3266726846886741e-1 7 Variable bound violation: 8.9075433662594991e-09 8.9075433662594991e-0 9 Complementarity.........: 9.0909090913713597e-08 1.4409400091641804e-0 6 Overall NLP error.......: 4.2045888000871561e-07 6.6644162462032336e-0 6

Number of objective function evaluations = 81 Number of objective gradient evaluations = 81 Number of equality constraint evaluations = 81 Number of inequality constraint evaluations = 81 Number of equality constraint Jacobian evaluations = 81 Number of inequality constraint Jacobian evaluations = 81 Number of Lagrangian Hessian evaluations = 80 Total seconds in IPOPT = 0.436

EXIT: Optimal Solution Found. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 50 Number of nonzeros in inequality constraint Jacobian.: 1200 Number of nonzeros in Lagrangian Hessian.............: 55

Total number of variables............................: 10 variables with only lower bounds: 0 variables with lower and upper bounds: 10 variables with only upper bounds: 0 Total number of equality constraints.................: 5 Total number of inequality constraints...............: 120 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 120 inequality constraints with only upper bounds: 0

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 1.2595275e+01 9.70e-01 7.66e-02 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 7.4290282e+00 0.00e+00 5.78e+01 -1.0 3.65e-01 - 3.61e-02 1.00e+0 0f 1 2 7.3851998e+00 0.00e+00 5.80e+00 -1.0 1.32e-02 2.0 1.00e+00 1.00e+0 0f 1 3 6.9491636e+00 0.00e+00 6.68e+00 -1.0 1.57e-01 - 7.88e-01 1.00e+0 0f 1 4 6.1022782e+00 0.00e+00 1.13e+01 -1.0 4.18e-01 - 1.00e+00 1.00e+0 0f 1 5 6.0717411e+00 0.00e+00 5.80e-01 -1.0 1.09e-02 1.5 1.00e+00 1.00e+0 0f 1 6 4.8382266e+00 0.00e+00 7.73e+00 -1.7 6.69e-01 - 4.49e-01 1.00e+0 0f 1 7 4.8222602e+00 0.00e+00 5.53e-01 -1.7 7.36e-03 1.0 1.00e+00 1.00e+0 0f 1 8 4.7626985e+00 0.00e+00 1.01e-01 -1.7 2.65e-02 0.6 1.00e+00 1.00e+0 0f 1 9 4.5136222e+00 0.00e+00 3.12e+00 -2.5 1.59e-01 0.1 7.91e-01 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 10 4.4716551e+00 0.00e+00 3.01e-01 -2.5 1.83e-02 0.5 1.00e+00 1.00e+0 0f 1 11 4.2875154e+00 0.00e+00 1.06e+00 -2.5 1.06e-01 0.0 1.00e+00 1.00e+0 0f 1 12 4.2373270e+00 0.00e+00 1.70e-01 -2.5 1.73e-02 0.5 1.00e+00 1.00e+0 0f 1 13 4.0979731e+00 0.00e+00 6.42e-01 -2.5 5.95e-02 -0.0 1.00e+00 1.00e+0 0f 1 14 2.8104315e+00 0.00e+00 1.48e+01 -2.5 3.02e+00 -0.5 1.91e-01 4.41e-0 1f 1 15 2.6662950e+00 0.00e+00 1.17e+00 -2.5 1.41e-01 -0.1 1.00e+00 1.00e+0 0f 1 16 1.8590501e+00 0.00e+00 4.21e+00 -2.5 6.21e-01 -0.5 1.00e+00 1.00e+0 0f 1 17 1.7500074e+00 0.00e+00 3.27e-01 -2.5 6.62e-02 -0.1 1.00e+00 1.00e+0 0f 1 18 1.3926176e+00 0.00e+00 4.25e-01 -2.5 1.99e-01 -0.6 1.00e+00 1.00e+0 0f 1 19 9.4820859e-01 0.00e+00 4.11e-01 -2.5 4.04e-01 -1.1 7.94e-01 1.00e+0 0f 1 iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 20 5.3435528e-01 0.00e+00 4.98e-01 -2.5 2.38e+00 - 6.35e-01 1.93e-0 1f 1 21 2.4569212e-01 0.00e+00 2.28e-01 -2.5 6.13e-01 - 1.00e+00 5.35e-0 1f 1 22 3.5117687e-01 0.00e+00 2.39e-01 -2.5 1.59e-01 - 5.48e-01 1.00e+0 0f 1 23 3.4202125e-01 0.00e+00 1.32e-02 -2.5 6.70e-02 - 1.00e+00 1.00e+0 0f 1 24 6.4606872e-02 0.00e+00 1.50e-01 -3.8 1.15e-01 - 9.92e-01 9.85e-0 1f 1 25 1.4902796e-02 0.00e+00 2.75e-03 -3.8 2.88e-02 - 1.00e+00 1.00e+0 0f 1 26 1.9499720e-02 0.00e+00 6.33e-05 -3.8 3.97e-03 - 1.00e+00 1.00e+0 0f 1 27 3.0836430e-04 0.00e+00 6.39e-04 -5.7 6.26e-03 - 1.00e+00 1.00e+0 0f 1 28 2.3981178e-04 0.00e+00 1.82e-08 -5.7 2.78e-05 - 1.00e+00 1.00e+0 0f 1 29 1.1789754e-05 0.00e+00 7.84e-08 -7.0 6.86e-05 - 1.00e+00 1.00e+0 0f 1

Number of Iterations....: 29

                               (scaled)                 (unscaled)

Objective...............: 1.1789754348677797e-05 1.1789754348677797e-0 5 Dual infeasibility......: 7.8413121968802421e-08 7.8413121968802421e-0 8 Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+0 0 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 1.2319818184323468e-07 1.2319818184323468e-0 7 Overall NLP error.......: 1.2319818184323468e-07 1.2319818184323468e-0 7

Number of objective function evaluations = 30 Number of objective gradient evaluations = 30 Number of equality constraint evaluations = 30 Number of inequality constraint evaluations = 30 Number of equality constraint Jacobian evaluations = 30 Number of inequality constraint Jacobian evaluations = 30 Number of Lagrangian Hessian evaluations = 29 Total seconds in IPOPT = 0.094

EXIT: Optimal Solution Found. This is Ipopt version 3.14.17, running with linear solver MUMPS 5.8.0.

Number of nonzeros in equality constraint Jacobian...: 0 Number of nonzeros in inequality constraint Jacobian.: 340560 Number of nonzeros in Lagrangian Hessian.............: 64980

Total number of variables............................: 360 variables with only lower bounds: 0 variables with lower and upper bounds: 300 variables with only upper bounds: 59 Total number of equality constraints.................: 0 Total number of inequality constraints...............: 946 inequality constraints with only lower bounds: 0 inequality constraints with lower and upper bounds: 0 inequality constraints with only upper bounds: 946

iter objective infpr infdu lg(mu) ||d|| lg(rg) alphadu alphap r ls 0 1.8536373e+00 7.80e+01 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+0 0 0 1 1.9171542e+00 7.80e+01 9.90e+03 -1.0 2.06e+01 6.0 5.18e-04 4.82e-0 4h 1

Number of Iterations....: 1

                               (scaled)                 (unscaled)

Objective...............: 1.9171542410561992e+00 1.9171542410561992e+0 0 Dual infeasibility......: 9.8991286008272818e+03 9.8991286008272818e+0 3 Constraint violation....: 7.7995725448164009e+01 7.7995725448164009e+0 1 Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+0 0 Complementarity.........: 1.0000000000000025e+09 1.0000000000000025e+0 9 Overall NLP error.......: 1.0000000000000025e+09 1.0000000000000025e+0 9

Number of objective function evaluations = 2 Number of objective gradient evaluations = 2 Number of equality constraint evaluations = 0 Number of inequality constraint evaluations = 2 Number of equality constraint Jacobian evaluations = 0 Number of inequality constraint Jacobian evaluations = 2 Number of Lagrangian Hessian evaluations = 1 Total seconds in IPOPT = 64.172

EXIT: Maximum wallclock time exceeded. Full results table for quadratic problems: 10×5 DataFrame Row │ problem n_vars secs solver retcode │ String Int64 Float64 String Symbol ─────┼────────────────────────────────────────────── 1 │ PRIMALC1 230 30.9028 Ipopt MaxTime 2 │ QPCBOEI1 384 30.2168 Ipopt MaxTime 3 │ DUAL2 96 17.4721 Ipopt Success 4 │ HS35 3 0.01092 Ipopt Success 5 │ GMNCASE2 175 42.8585 Ipopt MaxTime 6 │ QPNBOEI1 384 30.289 Ipopt MaxTime 7 │ TABLE8 1271 68.7647 Ipopt MaxTime 8 │ DUALC5 8 0.438994 Ipopt Success 9 │ DEGENQP 10 0.096483 Ipopt Success 10 │ LEUVEN7 360 64.2364 Ipopt MaxTime SUCCESS RATE ANALYSIS (Quadratic Problems): Total attempts: 10 Successful attempts: 10 Success rate: 100.0% Return code distribution: MaxTime: 6 occurrences Success: 4 occurrences Plotted quadratic problem results.





## Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai).

To locally run this benchmark, do the following commands:

using SciMLBenchmarks SciMLBenchmarks.weavefile("benchmarks/OptimizationCUTEst","CUTEstquadratic.jmd")


Computer Information:

Julia Version 1.10.10 Commit 95f30e51f41 (2025-06-27 09:51 UTC) Build Info: Official https://julialang.org/ release Platform Info: OS: Linux (x8664-linux-gnu) CPU: 128 × AMD EPYC 7502 32-Core Processor WORDSIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: JULIACPUTHREADS = 128 JULIADEPOTPATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953:


Package Information:

Status /cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/OptimizationCUTEst/Project.toml ⌃ [1b53aba6] CUTEst v1.3.2 ⌃ [a93c6f00] DataFrames v1.7.0 ⌃ [b6b21f68] Ipopt v1.10.6 ⌃ [b8f27783] MathOptInterface v1.42.1 ⌃ [a4795742] NLPModels v0.21.5 ⌅ [7f7a1694] Optimization v4.5.0 ⌃ [fd9f6733] OptimizationMOI v0.5.5 ⌅ [064b21be] OptimizationNLPModels v0.0.2 ⌃ [36348300] OptimizationOptimJL v0.4.3 ⌃ [42dfb2eb] OptimizationOptimisers v0.3.8 ⌃ [91a5bcdd] Plots v1.40.17 [31c91b34] SciMLBenchmarks v0.1.3 ⌃ [2913bbd2] StatsBase v0.34.6 ⌃ [f3b207a7] StatsPlots v0.15.7 [de0858da] Printf [10745b16] Statistics v1.10.0 Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use status --outdated Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to Pkg.resolve() or consider Pkg.update() if necessary.


And the full manifest:

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[e920d4aa] Xorgxcbutilcursorjll v0.1.5+0 [12413925] Xorgxcbutilimagejll v0.4.1+0 [2def613f] Xorgxcbutiljll v0.4.1+0 [975044d2] Xorgxcbutilkeysymsjll v0.4.1+0 [0d47668e] Xorgxcbutilrenderutiljll v0.3.10+0 [c22f9ab0] Xorgxcbutilwmjll v0.4.2+0 [35661453] Xorgxkbcompjll v1.4.7+0 [33bec58e] Xorgxkeyboardconfigjll v2.44.0+0 [c5fb5394] Xorgxtransjll v1.6.0+0 [8f1865be] ZeroMQjll v4.3.6+0 [3161d3a3] Zstdjll v1.5.7+1 [35ca27e7] eudevjll v3.2.14+0 [214eeab7] fzfjll v0.61.1+0 ⌃ [a4ae2306] libaomjll v3.12.1+0 [0ac62f75] libassjll v0.17.4+0 [1183f4f0] libdecorjll v0.2.2+0 [2db6ffa8] libevdevjll v1.13.4+0 [f638f0a6] libfdkaacjll v2.0.4+0 [36db933b] libinputjll v1.28.1+0 ⌃ [b53b4c65] libpngjll v1.6.50+0 [a9144af2] libsodiumjll v1.0.21+0 [f27f6e37] libvorbisjll v1.3.8+0 [009596ad] mtdevjll v1.1.7+0 ⌃ [1317d2d5] oneTBBjll v2022.0.0+0 ⌅ [1270edf5] x264jll v10164.0.1+0 [dfaa095f] x265jll v4.1.0+0 ⌃ [d8fb68d0] xkbcommonjll v1.9.2+0 [0dad84c5] ArgTools v1.1.1 [56f22d72] Artifacts [2a0f44e3] Base64 [ade2ca70] Dates [8ba89e20] Distributed [f43a241f] Downloads v1.6.0 [7b1f6079] FileWatching [9fa8497b] Future [b77e0a4c] InteractiveUtils [4af54fe1] LazyArtifacts [b27032c2] LibCURL v0.6.4 [76f85450] LibGit2 [8f399da3] Libdl [37e2e46d] LinearAlgebra [56ddb016] Logging [d6f4376e] Markdown [a63ad114] Mmap [ca575930] NetworkOptions v1.2.0 [44cfe95a] Pkg v1.10.0 [de0858da] Printf [9abbd945] Profile [3fa0cd96] REPL [9a3f8284] Random [ea8e919c] SHA v0.7.0 [9e88b42a] Serialization [1a1011a3] SharedArrays [6462fe0b] Sockets [2f01184e] SparseArrays v1.10.0 [10745b16] Statistics v1.10.0 [4607b0f0] SuiteSparse [fa267f1f] TOML v1.0.3 [a4e569a6] Tar v1.10.0 [8dfed614] Test [cf7118a7] UUIDs [4ec0a83e] Unicode [e66e0078] CompilerSupportLibrariesjll v1.1.1+0 [deac9b47] LibCURLjll v8.4.0+0 [e37daf67] LibGit2jll v1.6.4+0 [29816b5a] LibSSH2jll v1.11.0+1 [c8ffd9c3] MbedTLSjll v2.28.2+1 [14a3606d] MozillaCACertsjll v2023.1.10 [4536629a] OpenBLASjll v0.3.23+4 [05823500] OpenLibmjll v0.8.5+0 [efcefdf7] PCRE2jll v10.42.0+1 [bea87d4a] SuiteSparsejll v7.2.1+1 [83775a58] Zlibjll v1.2.13+1 [8e850b90] libblastrampolinejll v5.11.0+0 [8e850ede] nghttp2jll v1.52.0+1 [3f19e933] p7zip_jll v17.4.0+2 Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use status --outdated -m Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to Pkg.resolve() or consider Pkg.update() if necessary. ```