Core benchmark: glider

This page presents benchmark results for the glider problem across different platforms and configurations.

Note

The linear solver is MUMPS for all experiments.

Ubuntu Latest CPU

This benchmark suite evaluates optimal control problems on a standard CPU platform using GitHub Actions runners.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: ipopt, madnlp
Models: adnlp, exa, jump
Grid sizes: 200, 500, 1000, 2000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 500.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 15:16:44 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : runnervmg1sw1

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager

📦 Package status

Project CTBenchmarks v0.2.3
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
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  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
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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`

📈 Time vs Grid Size (Ubuntu Latest CPU)

🔁 Iterations vs CPU time (Ubuntu Latest CPU)

🧭 Solution: N = 200 (Ubuntu Latest CPU)

🧭 Solution: N = 500 (Ubuntu Latest CPU)

🧭 Solution: N = 1000 (Ubuntu Latest CPU)

🧭 Solution: N = 2000 (Ubuntu Latest CPU)

📊 Table of Results (Ubuntu Latest CPU)

Problem: `glider`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	6589.538	343	1248.896363	max
✓	200	`adnlp`	`madnlp`	1741.739	264	1248.809427	max
✓	200	`exa`	`ipopt`	5529.065	346	1248.896363	max
✓	200	`exa`	`madnlp`	938.796	297	1248.809427	max	✓
✓	200	`jump`	`ipopt`	8059.384	306	1248.896363	max
✓	200	`jump`	`madnlp`	3788.451	302	1248.809427	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	19211.533	878	1247.978430	max
✓	500	`adnlp`	`madnlp`	12631.093	685	1247.978430	max
✓	500	`exa`	`ipopt`	7191.654	690	1247.978430	max
✓	500	`exa`	`madnlp`	4062.014	543	1247.978430	max	✓
✓	500	`jump`	`ipopt`	23614.216	677	1247.978430	max
✓	500	`jump`	`madnlp`	24109.286	691	1247.978430	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	1000	`adnlp`	`ipopt`	52115.351	1000	457.072646	max
✓	1000	`adnlp`	`madnlp`	37903.055	712	1247.985216	max
✗	1000	`exa`	`ipopt`	24777.830	1000	455.152051	max
✓	1000	`exa`	`madnlp`	11102.152	727	1247.985216	max	✓
✗	1000	`jump`	`ipopt`	71379.625	1000	456.877476	max
✓	1000	`jump`	`madnlp`	48039.384	706	1247.985216	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	2000	`adnlp`	`ipopt`	126582.995	1000	715.426439	max
✓	2000	`adnlp`	`madnlp`	111239.456	850	1247.986999	max
✗	2000	`exa`	`ipopt`	61370.438	1000	651.292013	max
✓	2000	`exa`	`madnlp`	19475.893	532	1247.986999	max	✓
✗	2000	`jump`	`ipopt`	150474.218	1000	669.591393	max
✓	2000	`jump`	`madnlp`	88143.605	633	1247.986999	max

ℹ️ Log

Benchmarks results:

┌─ Problem: glider
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   8.059 s  | iters: 306   | obj: 1.248896e+03  (max) | CPU: 575.83 KiB
│  │  ✓ | adnlp    | time:   6.590 s  | iters: 343   | obj: 1.248896e+03  (max) | CPU: 334.58 MiB
│  │  ✓ | exa      | time:   5.529 s  | iters: 346   | obj: 1.248896e+03  (max) | CPU: 546.95 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  23.614 s  | iters: 677   | obj: 1.247978e+03  (max) | CPU:   1.25 MiB
│  │  ✓ | adnlp    | time:  19.212 s  | iters: 878   | obj: 1.247978e+03  (max) | CPU:   2.06 GiB
│  │  ✓ | exa      | time:   7.192 s  | iters: 690   | obj: 1.247978e+03  (max) | CPU: 1014.55 KiB
│  │
│  │  N = 1000
│  │  ✗ | jump     | time:  71.380 s  | iters: 1000  | obj: 4.568775e+02  (max) | CPU:   1.86 MiB
│  │  ✗ | adnlp    | time:  52.115 s  | iters: 1000  | obj: 4.570726e+02  (max) | CPU:   4.68 GiB
│  │  ✗ | exa      | time:  24.778 s  | iters: 1000  | obj: 4.551521e+02  (max) | CPU:   1.49 MiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 150.474 s  | iters: 1000  | obj: 6.695914e+02  (max) | CPU:   1.86 MiB
│  │  ✗ | adnlp    | time: 126.583 s  | iters: 1000  | obj: 7.154264e+02  (max) | CPU:   9.34 GiB
│  │  ✗ | exa      | time:  61.370 s  | iters: 1000  | obj: 6.512920e+02  (max) | CPU:   1.85 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   3.788 s  | iters: 302   | obj: 1.248809e+03  (max) | CPU:  71.30 MiB
│  │  ✓ | adnlp    | time:   1.742 s  | iters: 264   | obj: 1.248809e+03  (max) | CPU: 287.94 MiB
│  │  ✓ | exa      | time: 938.796 ms | iters: 297   | obj: 1.248809e+03  (max) | CPU:  31.28 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  24.109 s  | iters: 691   | obj: 1.247978e+03  (max) | CPU: 254.43 MiB
│  │  ✓ | adnlp    | time:  12.631 s  | iters: 685   | obj: 1.247978e+03  (max) | CPU:   1.76 GiB
│  │  ✓ | exa      | time:   4.062 s  | iters: 543   | obj: 1.247978e+03  (max) | CPU: 129.19 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  48.039 s  | iters: 706   | obj: 1.247985e+03  (max) | CPU: 507.92 MiB
│  │  ✓ | adnlp    | time:  37.903 s  | iters: 712   | obj: 1.247985e+03  (max) | CPU:   3.65 GiB
│  │  ✓ | exa      | time:  11.102 s  | iters: 727   | obj: 1.247985e+03  (max) | CPU: 315.92 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  88.144 s  | iters: 633   | obj: 1.247987e+03  (max) | CPU: 973.19 MiB
│  │  ✓ | adnlp    | time: 111.239 s  | iters: 850   | obj: 1.247987e+03  (max) | CPU:   8.81 GiB
│  │  ✓ | exa      | time:  19.476 s  | iters: 532   | obj: 1.247987e+03  (max) | CPU: 498.40 MiB
│  └─
└─

Moonshot CPU

Results on self-hosted CPU hardware.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: ipopt, madnlp
Models: adnlp, exa, jump
Grid sizes: 200, 500, 1000, 2000, 5000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 400.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 19:47:37 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : moonshot

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 144 × Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake-avx512)
Threads: 16 default, 0 interactive, 8 GC (on 144 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /scratch/github-actions/julia_depot
  LD_LIBRARY_PATH = /home/mschanen/local/lib:/home/mschanen/local/lib:
  JULIA_NUM_THREADS = 16

📦 Package status

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [91a5bcdd] Plots v1.41.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.19.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.0
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌃ [54762871] CTBase v0.16.2
  [790bbbee] CTDirect v0.17.4
  [1c39547c] CTFlows v0.8.9
  [34c4fa32] CTModels v0.6.9
  [32681960] CTParser v0.7.1
  [052768ef] CUDA v5.9.4
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.1
  [d360d2e6] ChainRulesCore v1.26.0
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [a93c6f00] DataFrames v1.8.1
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [ffbed154] DocStringExtensions v0.9.5
  [1037b233] ExaModels v0.9.2
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.15.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.0
  [069b7b12] FunctionWrappers v1.1.3
  [0c68f7d7] GPUArrays v11.2.6
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.7.4
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.18
  [42e2da0e] Grisu v1.0.2
  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
  [076d061b] HashArrayMappedTries v0.2.0
  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [5c8ed15e] LinearOperators v2.11.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [33e6dc65] MKL v0.9.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [2621e9c9] MadNLP v0.8.12
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.46.0
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
  [f4238b75] NLPModelsIpopt v0.11.0
  [e01155f1] NLPModelsModifiers v0.7.2
  [5da4648a] NVTX v1.0.1
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.1
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.0
  [43287f4e] PtrArrays v1.3.0
  [be4d8f0f] Quadmath v0.5.13
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [37e2e3b7] ReverseDiff v1.16.1
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.8
  [892a3eda] StringManipulation v0.4.1
  [856f2bd8] StructTypes v1.11.0
  [ec057cc2] StructUtils v2.6.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [a759f4b9] TimerOutputs v0.5.29
  [e689c965] Tracy v0.1.6
  [3bb67fe8] TranscodingStreams v0.11.3
  [5c2747f8] URIs v1.6.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
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  [41fe7b60] Unzip v0.2.0
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  [6e34b625] Bzip2_jll v1.0.9+0
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  [4ee394cb] CUDA_Driver_jll v13.0.2+0
  [76a88914] CUDA_Runtime_jll v0.19.2+0
  [4889d778] CUDSS_jll v0.7.1+0
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  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.7.3+0
  [b22a6f82] FFMPEG_jll v8.0.0+0
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  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.18+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.86.0+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [017b0a0e] HSL_jll v4.0.4+0
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  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
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  [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.41.2+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.100+0
  [e98f9f5b] NVTX_jll v3.2.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
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  [458c3c95] OpenSSL_jll v3.5.4+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.5.2+0
  [36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.8.2+2
  [629bc702] Qt6Declarative_jll v6.8.2+1
  [ce943373] Qt6ShaderTools_jll v6.8.2+1
  [e99dba38] Qt6Wayland_jll v6.8.2+2
⌅ [319450e9] SPRAL_jll v2025.5.20+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
⌅ [02c8fc9c] XML2_jll v2.13.9+0
  [ffd25f8a] XZ_jll v5.8.1+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.12+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.7+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.3+0
  [d1454406] Xorg_libXinerama_jll v1.1.6+0
  [ec84b674] Xorg_libXrandr_jll v1.5.5+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.18.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.3+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [1e29f10c] demumble_jll v1.3.0+0
  [35ca27e7] eudev_jll v3.2.14+0
  [214eeab7] fzf_jll v0.61.1+0
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  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.13.4+0
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  [4607b0f0] SuiteSparse
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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`

📈 Time vs Grid Size (Moonshot CPU)

🔁 Iterations vs CPU time (Moonshot CPU)

🧭 Solution: N = 200 (Moonshot CPU)

🧭 Solution: N = 500 (Moonshot CPU)

🧭 Solution: N = 1000 (Moonshot CPU)

🧭 Solution: N = 2000 (Moonshot CPU)

🧭 Solution: N = 5000 (Moonshot CPU)

📊 Table of Results (Moonshot CPU)

Problem: `glider`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	8878.254	399	1248.896363	max
✓	200	`adnlp`	`madnlp`	2139.229	282	1248.809427	max
✓	200	`exa`	`ipopt`	6895.696	378	1248.896363	max
✓	200	`exa`	`madnlp`	992.764	296	1248.809427	max	✓
✓	200	`jump`	`ipopt`	10236.560	358	1248.896363	max
✓	200	`jump`	`madnlp`	3623.791	292	1248.809427	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	17036.591	751	1247.978430	max
✓	500	`adnlp`	`madnlp`	15637.588	659	1247.978430	max
✓	500	`exa`	`ipopt`	8510.309	800	1247.978430	max
✓	500	`exa`	`madnlp`	5315.993	664	1247.978430	max	✓
✓	500	`jump`	`ipopt`	26032.979	714	1247.978430	max
✓	500	`jump`	`madnlp`	29912.473	692	1247.978430	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	1000	`adnlp`	`ipopt`	78818.002	1000	455.776274	max
✓	1000	`adnlp`	`madnlp`	33287.570	767	1247.985216	max
✗	1000	`exa`	`ipopt`	27527.302	1000	453.167621	max
✓	1000	`exa`	`madnlp`	10915.212	704	1247.985216	max	✓
✗	1000	`jump`	`ipopt`	80073.545	1000	460.244984	max
✓	1000	`jump`	`madnlp`	55901.545	720	1247.985216	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	2000	`adnlp`	`ipopt`	177447.796	1000	711.650818	max
✓	2000	`adnlp`	`madnlp`	32896.566	215	1247.986999	max
✗	2000	`exa`	`ipopt`	71432.296	1000	672.074630	max
✓	2000	`exa`	`madnlp`	21895.118	562	1247.986999	max	✓
✗	2000	`jump`	`ipopt`	181466.900	1000	656.546578	max
✓	2000	`jump`	`madnlp`	40419.486	218	1247.986999	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	5000	`adnlp`	`ipopt`	400014.560	772	663.167097	max
✓	5000	`adnlp`	`madnlp`	322587.377	858	1247.987504	max
✗	5000	`exa`	`ipopt`	223114.410	1000	671.451646	max
✓	5000	`exa`	`madnlp`	52215.116	475	1247.987504	max	✓
✗	5000	`jump`	`ipopt`	400458.759	733	685.264031	max
✓	5000	`jump`	`madnlp`	161949.529	395	1247.987504	max

ℹ️ Log

Benchmarks results:

┌─ Problem: glider
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  10.237 s  | iters: 358   | obj: 1.248896e+03  (max) | CPU: 677.20 KiB
│  │  ✓ | adnlp    | time:   8.878 s  | iters: 399   | obj: 1.248896e+03  (max) | CPU: 388.40 MiB
│  │  ✓ | exa      | time:   6.896 s  | iters: 378   | obj: 1.248896e+03  (max) | CPU: 582.39 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  26.033 s  | iters: 714   | obj: 1.247978e+03  (max) | CPU:   1.32 MiB
│  │  ✓ | adnlp    | time:  17.037 s  | iters: 751   | obj: 1.247978e+03  (max) | CPU:   1.76 GiB
│  │  ✓ | exa      | time:   8.510 s  | iters: 800   | obj: 1.247978e+03  (max) | CPU:   1.11 MiB
│  │
│  │  N = 1000
│  │  ✗ | jump     | time:  80.074 s  | iters: 1000  | obj: 4.602450e+02  (max) | CPU:   1.86 MiB
│  │  ✗ | adnlp    | time:  78.818 s  | iters: 1000  | obj: 4.557763e+02  (max) | CPU:   4.68 GiB
│  │  ✗ | exa      | time:  27.527 s  | iters: 1000  | obj: 4.531676e+02  (max) | CPU:   1.49 MiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 181.467 s  | iters: 1000  | obj: 6.565466e+02  (max) | CPU:   1.86 MiB
│  │  ✗ | adnlp    | time: 177.448 s  | iters: 1000  | obj: 7.116508e+02  (max) | CPU:   9.34 GiB
│  │  ✗ | exa      | time:  71.432 s  | iters: 1000  | obj: 6.720746e+02  (max) | CPU:   1.85 MiB
│  │
│  │  N = 5000
│  │  ✗ | jump     | time: 400.459 s  | iters: 733   | obj: 6.852640e+02  (max) | CPU:   1.36 MiB
│  │  ✗ | adnlp    | time: 400.015 s  | iters: 772   | obj: 6.631671e+02  (max) | CPU:  18.06 GiB
│  │  ✗ | exa      | time: 223.114 s  | iters: 1000  | obj: 6.714516e+02  (max) | CPU:   2.92 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   3.624 s  | iters: 292   | obj: 1.248809e+03  (max) | CPU:  70.43 MiB
│  │  ✓ | adnlp    | time:   2.139 s  | iters: 282   | obj: 1.248809e+03  (max) | CPU: 307.45 MiB
│  │  ✓ | exa      | time: 992.764 ms | iters: 296   | obj: 1.248809e+03  (max) | CPU:  31.46 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  29.912 s  | iters: 692   | obj: 1.247978e+03  (max) | CPU: 255.62 MiB
│  │  ✓ | adnlp    | time:  15.638 s  | iters: 659   | obj: 1.247978e+03  (max) | CPU:   1.70 GiB
│  │  ✓ | exa      | time:   5.316 s  | iters: 664   | obj: 1.247978e+03  (max) | CPU: 148.39 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  55.902 s  | iters: 720   | obj: 1.247985e+03  (max) | CPU: 513.68 MiB
│  │  ✓ | adnlp    | time:  33.288 s  | iters: 767   | obj: 1.247985e+03  (max) | CPU:   4.01 GiB
│  │  ✓ | exa      | time:  10.915 s  | iters: 704   | obj: 1.247985e+03  (max) | CPU: 306.62 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  40.419 s  | iters: 218   | obj: 1.247987e+03  (max) | CPU: 636.28 MiB
│  │  ✓ | adnlp    | time:  32.897 s  | iters: 215   | obj: 1.247987e+03  (max) | CPU:   2.33 GiB
│  │  ✓ | exa      | time:  21.895 s  | iters: 562   | obj: 1.247987e+03  (max) | CPU: 559.88 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time: 161.950 s  | iters: 395   | obj: 1.247988e+03  (max) | CPU:   1.87 GiB
│  │  ✓ | adnlp    | time: 322.587 s  | iters: 858   | obj: 1.247988e+03  (max) | CPU:  22.22 GiB
│  │  ✓ | exa      | time:  52.215 s  | iters: 475   | obj: 1.247988e+03  (max) | CPU:   1.08 GiB
│  └─
└─

Moonshot GPU

Results on self-hosted GPU hardware.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: madnlp
Models: exa, exa_gpu
Grid sizes: 1000, 5000, 10000, 20000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-6
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 1000.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 22:08:51 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : moonshot

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 144 × Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake-avx512)
Threads: 16 default, 0 interactive, 8 GC (on 144 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /scratch/github-actions/julia_depot
  LD_LIBRARY_PATH = /home/mschanen/local/lib:/home/mschanen/local/lib:
  JULIA_NUM_THREADS = 16

📦 Package status

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [91a5bcdd] Plots v1.41.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.19.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.0
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌃ [54762871] CTBase v0.16.2
  [790bbbee] CTDirect v0.17.4
  [1c39547c] CTFlows v0.8.9
  [34c4fa32] CTModels v0.6.9
  [32681960] CTParser v0.7.1
  [052768ef] CUDA v5.9.4
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.1
  [d360d2e6] ChainRulesCore v1.26.0
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [a93c6f00] DataFrames v1.8.1
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
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  [1037b233] ExaModels v0.9.2
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
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  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
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  [46192b85] GPUArraysCore v0.2.0
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  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
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  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
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  [33e6dc65] MKL v0.9.0
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  [1914dd2f] MacroTools v0.5.16
  [2621e9c9] MadNLP v0.8.12
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.46.0
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
  [f4238b75] NLPModelsIpopt v0.11.0
  [e01155f1] NLPModelsModifiers v0.7.2
  [5da4648a] NVTX v1.0.1
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.1
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.0
  [43287f4e] PtrArrays v1.3.0
  [be4d8f0f] Quadmath v0.5.13
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [37e2e3b7] ReverseDiff v1.16.1
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.8
  [892a3eda] StringManipulation v0.4.1
  [856f2bd8] StructTypes v1.11.0
  [ec057cc2] StructUtils v2.6.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
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⌅ [30392449] Pixman_jll v0.44.2+0
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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`

📈 Time vs Grid Size (Moonshot GPU)

🔁 Iterations vs CPU time (Moonshot GPU)

🧭 Solution: N = 1000 (Moonshot GPU)

🧭 Solution: N = 5000 (Moonshot GPU)

🧭 Solution: N = 10000 (Moonshot GPU)

🧭 Solution: N = 20000 (Moonshot GPU)

📊 Table of Results (Moonshot GPU)

Problem: `glider`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	11803.619	734	1247.985207	max	✓
✗	1000	`exa_gpu`	`madnlp`	15341.500	1000	442.685737	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	64440.289	522	1247.987459	max	✓
✗	5000	`exa_gpu`	`madnlp`	49405.985	1000	146.653771	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	119142.867	459	1247.987485	max	✓
✗	10000	`exa_gpu`	`madnlp`	81876.436	1000	577.244666	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	481829.221	889	1247.987411	max	✓
✗	20000	`exa_gpu`	`madnlp`	168571.251	1000	167.794436	max

ℹ️ Log

Benchmarks results:

┌─ Problem: glider
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  11.804 s  | iters: 734   | obj: 1.247985e+03  (max) | CPU: 318.62 MiB
│  │  ✗ | exa_gpu  | time:  15.341 s  | iters: 1000  | obj: 4.426857e+02  (max) | CPU: 885.274 MiB | GPU: 225.864 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  64.440 s  | iters: 522   | obj: 1.247987e+03  (max) | CPU:   1.16 GiB
│  │  ✗ | exa_gpu  | time:  49.406 s  | iters: 1000  | obj: 1.466538e+02  (max) | CPU: 839.929 MiB | GPU:  1.120 GiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 119.143 s  | iters: 459   | obj: 1.247987e+03  (max) | CPU:   2.02 GiB
│  │  ✗ | exa_gpu  | time:  81.876 s  | iters: 1000  | obj: 5.772447e+02  (max) | CPU:  1.142 GiB | GPU:  2.136 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 481.829 s  | iters: 889   | obj: 1.247987e+03  (max) | CPU:   7.40 GiB
│  │  ✗ | exa_gpu  | time: 168.571 s  | iters: 1000  | obj: 1.677944e+02  (max) | CPU: 940.681 MiB | GPU:  4.458 GiB
│  └─
└─