GitHub

Core GPU Benchmark

Note
  • The linear solver is MUMPS for all experiments.
  • Below you can find Dolan–Moré performance profiles comparing solver–model combinations on the set of optimal control problems and grid sizes. For a detailed explanation of how to read these profiles, see the Performance Profiles page.

Moonshot

This benchmark suite evaluates optimal control problems on GPU-accelerated hardware, focusing on large-scale problems.

⚙️ Configuration

  • Problems: beam, chain, double_oscillator, electric_vehicle, glider, jackson, robbins, rocket, vanderpol

  • Solvers: madnlp

  • Models: exa, exa_gpu

  • Grid sizes: 1000, 5000, 10000, 20000 discretization points

  • Discretization: midpoint method

  • Tolerance: 1.0e-8

  • Ipopt strategy: adaptive barrier parameter

  • Limits: 1000 iterations max, 2000.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-12-09 16:46:43 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : moonshot

You can download the exact environment used for this benchmark:

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

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
Project CTBenchmarks v0.3.1
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 v5.9.5
  [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 v0.4.0
  [91a5bcdd] Plots v1.41.2
  [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 but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
Project CTBenchmarks v0.3.1
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.20.0
  [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 v0.7.2
  [052768ef] CUDA v5.9.5
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.3
  [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 v11.3.1
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.7.5
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.19
  [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 v1.47.0
  [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 v1.6.1
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.4.0
  [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 v1.41.2
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.2
  [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 v0.3.9
  [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 v1.8.0
  [2913bbd2] StatsBase v0.34.9
  [892a3eda] StringManipulation v0.4.2
  [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
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [efce3f68] WoodburyMatrices v1.0.0
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [d1e2174e] CUDA_Compiler_jll v0.3.0+0
  [4ee394cb] CUDA_Driver_jll v13.0.2+0
  [76a88914] CUDA_Runtime_jll v0.19.2+0
  [4889d778] CUDSS_jll v0.7.1+0
  [83423d85] Cairo_jll v1.18.5+0
  [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
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.4.1+0
  [d2c73de3] GR_jll v0.73.19+1
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.86.2+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [017b0a0e] HSL_jll v4.0.4+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [e33a78d0] Hwloc_jll v2.12.2+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1900+0
  [aacddb02] JpegTurbo_jll v3.1.3+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [dad2f222] LLVMExtra_jll v0.0.38+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [ad6e5548] LibTracyClient_jll v0.9.1+6
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.2+0
  [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
  [656ef2d0] OpenBLAS32_jll v0.3.29+0
  [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
  [a4ae2306] libaom_jll v3.13.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.53+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

📈 Performance Profile GPU Time

Performance Profile Analysis

Dataset overview for core-moonshot-gpu:

  • Problems: 9 unique optimal control problems
  • Instances: 36
  • Solver combos: 2

Profile configuration:

  • Instance definition: (problem, grid_size)
  • Solver combos definition: (model, solver)
  • Criterion: CPU time
  • Successful runs: 67/72 (93.1%)
  • Successful instances: 35/36 (97.2%)
  • Unsuccessful instances (no solver converged):
    • glider, 5000

Robustness (% of instances solved):

  • (exa, madnlp): 97.2%
  • (exa_gpu, madnlp): 88.9%

Efficiency (% of instances where fastest):

  • (exa, madnlp): 33.3%
  • (exa_gpu, madnlp): 63.9%

Most robust: (exa, madnlp) solved 97.2% of instances.

Most efficient: (exa_gpu, madnlp) was fastest on 63.9% of instances.

📈 Performance Profile Iterations

Performance Profile Analysis

Dataset overview for core-moonshot-gpu:

  • Problems: 9 unique optimal control problems
  • Instances: 36
  • Solver combos: 2

Profile configuration:

  • Instance definition: (problem, grid_size)
  • Solver combos definition: (model, solver)
  • Criterion: Iterations
  • Successful runs: 67/72 (93.1%)
  • Successful instances: 35/36 (97.2%)
  • Unsuccessful instances (no solver converged):
    • glider, 5000

Robustness (% of instances solved):

  • (exa, madnlp): 97.2%
  • (exa_gpu, madnlp): 88.9%

Efficiency (% of instances where fastest):

  • (exa, madnlp): 91.7%
  • (exa_gpu, madnlp): 19.4%

Most robust: (exa, madnlp) solved 97.2% of instances.

Most efficient: (exa, madnlp) was fastest on 91.7% of instances.

📊 Tables of Results


SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓1000examadnlp74.455268.888914min✓
✓1000exa_gpumadnlp277.577488.888302min
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓5000examadnlp1195.754798.888892min
✓5000exa_gpumadnlp947.4181388.885839min✓
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓10000examadnlp5897.5971758.888893min
✓10000exa_gpumadnlp1879.4742348.882791min✓
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓20000examadnlp13832.8231898.888898min
✓20000exa_gpumadnlp2628.2463818.876698min✓
 
Benchmarks results:

┌─ Problem: beam
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  74.455 ms | iters: 26    | obj: 8.888914e+00  (min) | CPU:   8.89 MiB
│  │  ✓ | exa_gpu  | time: 277.577 ms | iters: 48    | obj: 8.888302e+00  (min) | CPU: 16.613 MiB | GPU: 12.101 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.196 s  | iters: 79    | obj: 8.888892e+00  (min) | CPU:  97.02 MiB
│  │  ✓ | exa_gpu  | time: 947.418 ms | iters: 138   | obj: 8.885839e+00  (min) | CPU: 47.271 MiB | GPU: 94.855 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   5.898 s  | iters: 175   | obj: 8.888893e+00  (min) | CPU: 391.56 MiB
│  │  ✓ | exa_gpu  | time:   1.879 s  | iters: 234   | obj: 8.882791e+00  (min) | CPU: 91.258 MiB | GPU: 262.464 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  13.833 s  | iters: 189   | obj: 8.888898e+00  (min) | CPU: 841.47 MiB
│  │  ✓ | exa_gpu  | time:   2.628 s  | iters: 381   | obj: 8.876698e+00  (min) | CPU: 125.664 MiB | GPU: 747.316 MiB
│  └─
└─

┌─ Problem: chain
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  60.927 ms | iters: 14    | obj: 5.068480e+00  (min) | CPU:   6.74 MiB
│  │  ✓ | exa_gpu  | time: 125.344 ms | iters: 15    | obj: 5.068452e+00  (min) | CPU:  7.756 MiB | GPU: 14.348 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 476.996 ms | iters: 13    | obj: 5.068480e+00  (min) | CPU:  30.89 MiB
│  │  ✓ | exa_gpu  | time: 175.897 ms | iters: 16    | obj: 5.068339e+00  (min) | CPU: 10.799 MiB | GPU: 72.133 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.049 s  | iters: 13    | obj: 5.068480e+00  (min) | CPU:  61.26 MiB
│  │  ✓ | exa_gpu  | time:  29.423 s  | iters: 439   | obj: 5.068201e+00  (min) | CPU:  1.633 GiB | GPU: 576.439 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   3.589 s  | iters: 14    | obj: 5.068480e+00  (min) | CPU: 125.07 MiB
│  │  ✓ | exa_gpu  | time: 302.681 ms | iters: 15    | obj: 5.067922e+00  (min) | CPU: 19.882 MiB | GPU: 286.336 MiB
│  └─
└─

┌─ Problem: double_oscillator
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  41.658 ms | iters: 6     | obj: 9.110011e-04  (min) | CPU:  10.65 MiB
│  │  ✓ | exa_gpu  | time:  90.534 ms | iters: 6     | obj: 9.106227e-04  (min) | CPU:  6.238 MiB | GPU: 29.634 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 468.704 ms | iters: 6     | obj: 9.110335e-04  (min) | CPU:  51.32 MiB
│  │  ✓ | exa_gpu  | time: 218.805 ms | iters: 6     | obj: 9.091470e-04  (min) | CPU: 14.877 MiB | GPU: 148.459 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.000 s  | iters: 6     | obj: 9.110345e-04  (min) | CPU: 102.16 MiB
│  │  ✓ | exa_gpu  | time: 244.341 ms | iters: 6     | obj: 9.072690e-04  (min) | CPU: 20.132 MiB | GPU: 296.003 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.358 s  | iters: 6     | obj: 9.110348e-04  (min) | CPU: 203.85 MiB
│  │  ✓ | exa_gpu  | time: 354.128 ms | iters: 6     | obj: 9.035310e-04  (min) | CPU: 36.184 MiB | GPU: 591.891 MiB
│  └─
└─

┌─ Problem: electric_vehicle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  18.819 ms | iters: 4     | obj: 1.228583e+03  (min) | CPU:   4.95 MiB
│  │  ✓ | exa_gpu  | time:  92.246 ms | iters: 11    | obj: 1.228577e+03  (min) | CPU:  6.185 MiB | GPU: 13.167 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 171.911 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  23.54 MiB
│  │  ✓ | exa_gpu  | time: 129.296 ms | iters: 11    | obj: 1.228551e+03  (min) | CPU:  9.499 MiB | GPU: 65.806 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 380.696 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  46.63 MiB
│  │  ✓ | exa_gpu  | time: 137.367 ms | iters: 10    | obj: 1.228521e+03  (min) | CPU: 12.157 MiB | GPU: 130.933 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 852.533 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  92.80 MiB
│  │  ✓ | exa_gpu  | time: 191.228 ms | iters: 10    | obj: 1.228463e+03  (min) | CPU: 19.469 MiB | GPU: 261.839 MiB
│  └─
└─

┌─ Problem: glider
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  10.738 s  | iters: 729   | obj: -1.247985e+03 (min) | CPU: 314.44 MiB
│  │  ✗ | exa_gpu  | time:  13.531 s  | iters: 1000  | obj: -2.314292e+02 (min) | CPU: 854.804 MiB | GPU: 224.246 MiB
│  │
│  │  N = 5000
│  │  ✗ | exa      | time: 114.709 s  | iters: 1000  | obj: -1.215926e+03 (min) | CPU:   2.10 GiB
│  │  ✗ | exa_gpu  | time:   6.879 s  | iters: 128   | obj: -1.013713e+02 (min) | CPU: 143.923 MiB | GPU: 373.914 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 171.780 s  | iters: 763   | obj: -1.247988e+03 (min) | CPU:   3.22 GiB
│  │  ✗ | exa_gpu  | time:  10.744 s  | iters: 115   | obj: -1.083643e+02 (min) | CPU: 138.935 MiB | GPU: 725.767 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 230.370 s  | iters: 527   | obj: -1.247988e+03 (min) | CPU:   5.10 GiB
│  │  ✗ | exa_gpu  | time: 174.403 s  | iters: 1000  | obj: -3.695779e+02 (min) | CPU: 865.837 MiB | GPU:  4.378 GiB
│  └─
└─

┌─ Problem: jackson
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 100.998 ms | iters: 23    | obj: -1.918150e-01 (min) | CPU:  20.88 MiB
│  │  ✓ | exa_gpu  | time: 175.808 ms | iters: 22    | obj: -1.918374e-01 (min) | CPU: 10.130 MiB | GPU: 26.396 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 697.461 ms | iters: 21    | obj: -1.918128e-01 (min) | CPU:  96.91 MiB
│  │  ✓ | exa_gpu  | time: 266.524 ms | iters: 25    | obj: -1.919247e-01 (min) | CPU: 16.844 MiB | GPU: 134.356 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.465 s  | iters: 21    | obj: -1.918111e-01 (min) | CPU: 193.26 MiB
│  │  ✓ | exa_gpu  | time: 319.805 ms | iters: 24    | obj: -1.920350e-01 (min) | CPU: 23.312 MiB | GPU: 266.923 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   3.335 s  | iters: 20    | obj: -1.918079e-01 (min) | CPU: 375.57 MiB
│  │  ✓ | exa_gpu  | time: 549.393 ms | iters: 21    | obj: -1.922558e-01 (min) | CPU: 35.987 MiB | GPU: 523.752 MiB
│  └─
└─

┌─ Problem: robbins
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 299.890 ms | iters: 44    | obj: 1.943317e+01  (min) | CPU:  14.32 MiB
│  │  ✓ | exa_gpu  | time: 368.758 ms | iters: 44    | obj: 1.943298e+01  (min) | CPU: 18.419 MiB | GPU: 18.398 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   2.517 s  | iters: 75    | obj: 1.943184e+01  (min) | CPU: 100.74 MiB
│  │  ✓ | exa_gpu  | time: 492.927 ms | iters: 48    | obj: 1.943093e+01  (min) | CPU: 21.902 MiB | GPU: 93.877 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   4.205 s  | iters: 63    | obj: 1.943181e+01  (min) | CPU: 176.54 MiB
│  │  ✓ | exa_gpu  | time:   1.067 s  | iters: 95    | obj: 1.942999e+01  (min) | CPU: 42.458 MiB | GPU: 236.838 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  11.831 s  | iters: 71    | obj: 1.943181e+01  (min) | CPU: 386.90 MiB
│  │  ✓ | exa_gpu  | time:   1.255 s  | iters: 91    | obj: 1.942819e+01  (min) | CPU: 49.573 MiB | GPU: 464.901 MiB
│  └─
└─

┌─ Problem: rocket
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 144.374 ms | iters: 23    | obj: -1.012833e+00 (min) | CPU:  21.07 MiB
│  │  ✓ | exa_gpu  | time: 346.080 ms | iters: 24    | obj: -1.012870e+00 (min) | CPU: 12.503 MiB | GPU: 34.870 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 941.435 ms | iters: 21    | obj: -1.012820e+00 (min) | CPU:  98.57 MiB
│  │  ✓ | exa_gpu  | time: 846.136 ms | iters: 27    | obj: -1.013000e+00 (min) | CPU: 21.260 MiB | GPU: 176.718 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.362 s  | iters: 24    | obj: -1.012824e+00 (min) | CPU: 210.32 MiB
│  │  ✓ | exa_gpu  | time:   1.535 s  | iters: 27    | obj: -1.013162e+00 (min) | CPU: 30.619 MiB | GPU: 353.259 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   4.141 s  | iters: 21    | obj: -1.012767e+00 (min) | CPU: 392.57 MiB
│  │  ✓ | exa_gpu  | time:   2.656 s  | iters: 29    | obj: -1.013484e+00 (min) | CPU: 50.085 MiB | GPU: 712.702 MiB
│  └─
└─

┌─ Problem: vanderpol
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  23.107 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:   5.41 MiB
│  │  ✓ | exa_gpu  | time: 116.645 ms | iters: 7     | obj: 1.047787e+00  (min) | CPU:  6.183 MiB | GPU: 13.701 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 149.856 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  25.29 MiB
│  │  ✓ | exa_gpu  | time: 141.503 ms | iters: 7     | obj: 1.047710e+00  (min) | CPU:  9.642 MiB | GPU: 68.475 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 320.819 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  50.14 MiB
│  │  ✓ | exa_gpu  | time: 191.049 ms | iters: 8     | obj: 1.047613e+00  (min) | CPU: 14.309 MiB | GPU: 137.547 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 774.128 ms | iters: 5     | obj: 1.047807e+00  (min) | CPU: 102.12 MiB
│  │  ✓ | exa_gpu  | time: 231.373 ms | iters: 7     | obj: 1.047420e+00  (min) | CPU: 21.355 MiB | GPU: 273.683 MiB
│  └─
└─

KKT

This benchmark suite evaluates optimal control problems on the KKT runner.

⚙️ Configuration

  • Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol, brachistochrone, balanced_field, bryson_denham, mountain_car

  • Solvers: madnlp

  • Models: exa, exa_gpu

  • Grid sizes: 1000, 5000, 10000, 20000 discretization points

  • Discretization: midpoint method

  • Tolerance: 1.0e-8

  • Ipopt strategy: adaptive barrier parameter

  • Limits: 1000 iterations max, 2000.0s wall time

🖥️ Environment

📅 Timestamp     : 2026-03-05 09:50:16 UTC
🔧 Julia version : 1.11.9
💻 OS            : Linux
🖥️ Machine       : kkt.mcs.anl.gov

You can download the exact environment used for this benchmark:

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

Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 192 × INTEL(R) XEON(R) PLATINUM 8568Y+
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, sapphirerapids)
Threads: 1 default, 0 interactive, 1 GC (on 192 virtual cores)
Environment:
  JULIA_CUDSS_LIBRARY_PATH = /software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib
  JULIA_LOAD_PATH = @:@v#.#:@stdlib:/software/julia/environments/v1.12
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /storage/mschanen/github-actions/julia_depot
  LD_LIBRARY_PATH = /software/julia/julia_binaries/julia-1.12/lib:/software/mpich-ofi/lib:/software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib:/usr/local/cuda/lib
Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌅ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.7
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.14.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.2
⌃ [5f98b655] OptimalControl v1.1.8-beta.3
  [59046045] OptimalControlProblems v0.4.0 `https://github.com/control-toolbox/OptimalControlProblems.jl#206-dev-test-all-new-problems-with-gpu`
  [91a5bcdd] Plots v1.41.6
  [10745b16] Statistics v1.11.1
  [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 ⌃ 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`
Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.21.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.5.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.1
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌅ [54762871] CTBase v0.16.2
⌅ [790bbbee] CTDirect v0.17.5-beta
⌃ [1c39547c] CTFlows v0.8.12-beta
⌅ [34c4fa32] CTModels v0.6.10-beta.2
⌃ [32681960] CTParser v0.8.2-beta.6
  [052768ef] CUDA v5.9.7
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.7
  [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 v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.1
  [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 v0.9.3
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.16.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.2
  [069b7b12] FunctionWrappers v1.1.3
  [0c68f7d7] GPUArrays v11.4.1
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.8.2
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.24
  [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 v1.14.1
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
  [63c18a36] KernelAbstractions v0.9.40
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.6
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [5c8ed15e] LinearOperators v2.13.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [33e6dc65] MKL v0.9.1
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
⌅ [2621e9c9] MadNLP v0.8.12
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.49.0
  [739be429] MbedTLS v1.1.10
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.11
  [f4238b75] NLPModelsIpopt v0.11.2
  [e01155f1] NLPModelsModifiers v0.7.4
  [5da4648a] NVTX v1.0.3
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.1
⌃ [5f98b655] OptimalControl v1.1.8-beta.3
  [59046045] OptimalControlProblems v0.4.0 `https://github.com/control-toolbox/OptimalControlProblems.jl#206-dev-test-all-new-problems-with-gpu`
  [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 v1.41.6
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.2
  [08abe8d2] PrettyTables v3.2.3
  [43287f4e] PtrArrays v1.4.0
  [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 v1.16.2
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.9
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.10
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.2.1
  [0a514795] SparseMatrixColorings v0.4.24
  [276daf66] SpecialFunctions v2.7.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.17
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.10
  [892a3eda] StringManipulation v0.4.4
  [ec057cc2] StructUtils v2.6.3
  [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
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [efce3f68] WoodburyMatrices v1.1.0
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [d1e2174e] CUDA_Compiler_jll v0.4.1+1
  [4ee394cb] CUDA_Driver_jll v13.1.0+2
⌅ [76a88914] CUDA_Runtime_jll v0.19.2+0
  [4889d778] CUDSS_jll v0.7.1+0
  [83423d85] Cairo_jll v1.18.5+1
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.7.3+0
  [b22a6f82] FFMPEG_jll v8.0.1+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.4.1+0
  [d2c73de3] GR_jll v0.73.24+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.86.3+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [017b0a0e] HSL_jll v4.0.4+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [e33a78d0] Hwloc_jll v2.13.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1901+0
  [aacddb02] JpegTurbo_jll v3.1.4+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [dad2f222] LLVMExtra_jll v0.0.38+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [ad6e5548] LibTracyClient_jll v0.13.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.3+0
  [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.41.3+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.200+0
  [e98f9f5b] NVTX_jll v3.2.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.30+0
  [458c3c95] OpenSSL_jll v3.5.5+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.10.2+1
  [629bc702] Qt6Declarative_jll v6.10.2+1
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [319450e9] SPRAL_jll v2025.9.18+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 v5.8.2+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+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 v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.3+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+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 v1.2.0+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
  [a4ae2306] libaom_jll v3.13.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.55+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [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`

📈 Performance Profile GPU Time

Performance Profile Analysis

Dataset overview for core-kkt:

  • Problems: 17 unique optimal control problems
  • Instances: 68
  • Solver combos: 2

Profile configuration:

  • Instance definition: (problem, grid_size)
  • Solver combos definition: (model, solver)
  • Criterion: CPU time
  • Successful runs: 134/136 (98.5%)
  • Successful instances: 68/68 (100.0%)
  • Unsuccessful instances: none (every instance had at least one successful run)

Robustness (% of instances solved):

  • (exa, madnlp): 98.5%
  • (exa_gpu, madnlp): 98.5%

Efficiency (% of instances where fastest):

  • (exa, madnlp): 27.9%
  • (exa_gpu, madnlp): 72.1%

Most robust: 2 combinations tied at 98.5%.

Most efficient: (exa_gpu, madnlp) was fastest on 72.1% of instances.

📈 Performance Profile Iterations

Performance Profile Analysis

Dataset overview for core-kkt:

  • Problems: 17 unique optimal control problems
  • Instances: 68
  • Solver combos: 2

Profile configuration:

  • Instance definition: (problem, grid_size)
  • Solver combos definition: (model, solver)
  • Criterion: Iterations
  • Successful runs: 134/136 (98.5%)
  • Successful instances: 68/68 (100.0%)
  • Unsuccessful instances: none (every instance had at least one successful run)

Robustness (% of instances solved):

  • (exa, madnlp): 98.5%
  • (exa_gpu, madnlp): 98.5%

Efficiency (% of instances where fastest):

  • (exa, madnlp): 67.6%
  • (exa_gpu, madnlp): 39.7%

Most robust: 2 combinations tied at 98.5%.

Most efficient: (exa, madnlp) was fastest on 67.6% of instances.

📊 Tables of Results


SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓1000examadnlp129.90125771.007821min✓
✓1000exa_gpumadnlp289.06330770.995683min
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✗5000examadnlp31579.8001000883.592382min
✓5000exa_gpumadnlp1524.02840770.947303min✓
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓10000examadnlp4480.59052771.007836min
✓10000exa_gpumadnlp2226.68936770.886786min✓
SuccessNModelSolverTime (ms)ItersObjectiveCriterionBest
✓20000examadnlp9378.73250771.007861min
✓20000exa_gpumadnlp5374.60749770.766066min✓
 
Benchmarks results:

┌─ Problem: beam
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  44.575 ms | iters: 26    | obj: 8.888914e+00  (min) | CPU:   8.89 MiB
│  │  ✓ | exa_gpu  | time: 191.085 ms | iters: 48    | obj: 8.888302e+00  (min) | CPU: 16.619 MiB | GPU: 12.065 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 731.085 ms | iters: 79    | obj: 8.888892e+00  (min) | CPU:  97.02 MiB
│  │  ✓ | exa_gpu  | time: 585.251 ms | iters: 139   | obj: 8.885839e+00  (min) | CPU: 48.059 MiB | GPU: 94.741 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   3.116 s  | iters: 175   | obj: 8.888893e+00  (min) | CPU: 391.50 MiB
│  │  ✓ | exa_gpu  | time:   1.362 s  | iters: 266   | obj: 8.882791e+00  (min) | CPU: 99.561 MiB | GPU: 285.392 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   7.164 s  | iters: 189   | obj: 8.888898e+00  (min) | CPU: 841.46 MiB
│  │  ✓ | exa_gpu  | time:   1.899 s  | iters: 414   | obj: 8.876698e+00  (min) | CPU: 134.679 MiB | GPU: 793.996 MiB
│  └─
└─

┌─ Problem: chain
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  36.757 ms | iters: 14    | obj: 5.068480e+00  (min) | CPU:   6.74 MiB
│  │  ✓ | exa_gpu  | time:  88.766 ms | iters: 15    | obj: 5.068452e+00  (min) | CPU:  7.761 MiB | GPU: 14.326 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 298.970 ms | iters: 13    | obj: 5.068480e+00  (min) | CPU:  30.89 MiB
│  │  ✓ | exa_gpu  | time: 126.469 ms | iters: 16    | obj: 5.068339e+00  (min) | CPU: 10.925 MiB | GPU: 72.023 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 611.178 ms | iters: 13    | obj: 5.068480e+00  (min) | CPU:  61.26 MiB
│  │  ✓ | exa_gpu  | time: 422.304 ms | iters: 51    | obj: 5.068197e+00  (min) | CPU: 33.574 MiB | GPU: 176.652 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.089 s  | iters: 14    | obj: 5.068480e+00  (min) | CPU: 125.07 MiB
│  │  ✓ | exa_gpu  | time: 204.581 ms | iters: 15    | obj: 5.067922e+00  (min) | CPU: 19.887 MiB | GPU: 286.056 MiB
│  └─
└─

┌─ Problem: double_oscillator
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  24.124 ms | iters: 6     | obj: 9.110011e-04  (min) | CPU:  10.65 MiB
│  │  ✓ | exa_gpu  | time: 115.200 ms | iters: 6     | obj: 9.106227e-04  (min) | CPU:  5.805 MiB | GPU: 29.597 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 295.077 ms | iters: 6     | obj: 9.110335e-04  (min) | CPU:  51.32 MiB
│  │  ✓ | exa_gpu  | time: 134.800 ms | iters: 6     | obj: 9.091471e-04  (min) | CPU: 14.889 MiB | GPU: 148.157 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 613.176 ms | iters: 6     | obj: 9.110345e-04  (min) | CPU: 102.16 MiB
│  │  ✓ | exa_gpu  | time: 146.024 ms | iters: 6     | obj: 9.072690e-04  (min) | CPU: 20.201 MiB | GPU: 295.844 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   1.417 s  | iters: 6     | obj: 9.110348e-04  (min) | CPU: 203.85 MiB
│  │  ✓ | exa_gpu  | time: 242.082 ms | iters: 6     | obj: 9.035309e-04  (min) | CPU: 36.195 MiB | GPU: 591.571 MiB
│  └─
└─

┌─ Problem: electric_vehicle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  10.914 ms | iters: 4     | obj: 1.228583e+03  (min) | CPU:   4.95 MiB
│  │  ✓ | exa_gpu  | time:  62.663 ms | iters: 11    | obj: 1.228577e+03  (min) | CPU:  6.128 MiB | GPU: 13.152 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 113.830 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  23.54 MiB
│  │  ✓ | exa_gpu  | time:  83.919 ms | iters: 11    | obj: 1.228551e+03  (min) | CPU:  9.564 MiB | GPU: 65.721 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 242.698 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  46.63 MiB
│  │  ✓ | exa_gpu  | time:  93.614 ms | iters: 10    | obj: 1.228521e+03  (min) | CPU: 12.344 MiB | GPU: 130.823 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 518.973 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  92.81 MiB
│  │  ✓ | exa_gpu  | time: 316.410 ms | iters: 10    | obj: 1.228463e+03  (min) | CPU: 19.292 MiB | GPU: 261.610 MiB
│  └─
└─

┌─ Problem: glider
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 863.147 ms | iters: 102   | obj: -1.247985e+03 (min) | CPU:  62.93 MiB
│  │  ✓ | exa_gpu  | time: 595.462 ms | iters: 30    | obj: -1.247986e+03 (min) | CPU: 38.206 MiB | GPU: 55.249 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 772.646 ms | iters: 16    | obj: -1.247987e+03 (min) | CPU: 122.65 MiB
│  │  ✓ | exa_gpu  | time:   3.619 s  | iters: 92    | obj: -1.247990e+03 (min) | CPU: 98.110 MiB | GPU: 328.963 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.703 s  | iters: 16    | obj: -1.247988e+03 (min) | CPU: 244.58 MiB
│  │  ✓ | exa_gpu  | time:   1.697 s  | iters: 22    | obj: -1.247993e+03 (min) | CPU: 58.597 MiB | GPU: 537.162 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   3.730 s  | iters: 17    | obj: -1.247988e+03 (min) | CPU: 496.23 MiB
│  │  ✓ | exa_gpu  | time:   2.706 s  | iters: 20    | obj: -1.247998e+03 (min) | CPU: 92.262 MiB | GPU:  1.042 GiB
│  └─
└─

┌─ Problem: insurance
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:   3.447 s  | iters: 313   | obj: -2.058233e+00 (min) | CPU: 282.43 MiB
│  │  ✓ | exa_gpu  | time:   2.944 s  | iters: 448   | obj: -2.058242e+00 (min) | CPU: 193.963 MiB | GPU: 180.049 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  33.535 s  | iters: 757   | obj: -2.059098e+00 (min) | CPU:   3.07 GiB
│  │  ✓ | exa_gpu  | time:   6.901 s  | iters: 442   | obj: -2.059144e+00 (min) | CPU: 248.964 MiB | GPU: 894.567 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  68.372 s  | iters: 573   | obj: -2.059342e+00 (min) | CPU:   4.64 GiB
│  │  ✓ | exa_gpu  | time:  13.416 s  | iters: 504   | obj: -2.059436e+00 (min) | CPU: 293.081 MiB | GPU:  1.945 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 187.350 s  | iters: 705   | obj: -2.059516e+00 (min) | CPU:  11.86 GiB
│  │  ✓ | exa_gpu  | time:  28.060 s  | iters: 716   | obj: -2.059776e+00 (min) | CPU: 418.306 MiB | GPU:  5.267 GiB
│  └─
└─

┌─ Problem: jackson
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  62.070 ms | iters: 23    | obj: -1.918150e-01 (min) | CPU:  20.88 MiB
│  │  ✓ | exa_gpu  | time: 101.388 ms | iters: 22    | obj: -1.918374e-01 (min) | CPU: 10.195 MiB | GPU: 26.360 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 410.546 ms | iters: 21    | obj: -1.918128e-01 (min) | CPU:  96.91 MiB
│  │  ✓ | exa_gpu  | time: 167.446 ms | iters: 25    | obj: -1.919247e-01 (min) | CPU: 16.848 MiB | GPU: 134.146 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 847.248 ms | iters: 21    | obj: -1.918111e-01 (min) | CPU: 193.26 MiB
│  │  ✓ | exa_gpu  | time: 202.525 ms | iters: 24    | obj: -1.920350e-01 (min) | CPU: 23.377 MiB | GPU: 266.615 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   1.797 s  | iters: 20    | obj: -1.918079e-01 (min) | CPU: 375.57 MiB
│  │  ✓ | exa_gpu  | time: 358.025 ms | iters: 21    | obj: -1.922558e-01 (min) | CPU: 35.993 MiB | GPU: 523.307 MiB
│  └─
└─

┌─ Problem: robbins
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 183.457 ms | iters: 44    | obj: 1.943317e+01  (min) | CPU:  14.32 MiB
│  │  ✓ | exa_gpu  | time: 195.002 ms | iters: 44    | obj: 1.943298e+01  (min) | CPU: 18.421 MiB | GPU: 18.336 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.219 s  | iters: 75    | obj: 1.943184e+01  (min) | CPU: 100.74 MiB
│  │  ✓ | exa_gpu  | time: 246.295 ms | iters: 47    | obj: 1.943093e+01  (min) | CPU: 22.073 MiB | GPU: 93.070 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.147 s  | iters: 63    | obj: 1.943181e+01  (min) | CPU: 176.54 MiB
│  │  ✓ | exa_gpu  | time: 559.073 ms | iters: 97    | obj: 1.942999e+01  (min) | CPU: 42.863 MiB | GPU: 238.016 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   5.562 s  | iters: 71    | obj: 1.943181e+01  (min) | CPU: 386.90 MiB
│  │  ✓ | exa_gpu  | time: 602.137 ms | iters: 88    | obj: 1.942819e+01  (min) | CPU: 47.758 MiB | GPU: 456.831 MiB
│  └─
└─

┌─ Problem: robot
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 312.799 ms | iters: 23    | obj: 9.140917e+00  (min) | CPU:  37.94 MiB
│  │  ✓ | exa_gpu  | time: 387.340 ms | iters: 29    | obj: 9.140745e+00  (min) | CPU: 18.835 MiB | GPU: 58.809 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   4.047 s  | iters: 50    | obj: 9.140949e+00  (min) | CPU: 311.78 MiB
│  │  ✓ | exa_gpu  | time:   2.643 s  | iters: 55    | obj: 9.140129e+00  (min) | CPU: 44.905 MiB | GPU: 337.881 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   5.629 s  | iters: 34    | obj: 9.140939e+00  (min) | CPU: 465.04 MiB
│  │  ✓ | exa_gpu  | time:   4.003 s  | iters: 54    | obj: 9.139277e+00  (min) | CPU: 55.292 MiB | GPU: 658.198 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  25.862 s  | iters: 41    | obj: 9.140966e+00  (min) | CPU:   1.12 GiB
│  │  ✓ | exa_gpu  | time:   4.980 s  | iters: 31    | obj: 9.137650e+00  (min) | CPU: 71.859 MiB | GPU:  1.157 GiB
│  └─
└─

┌─ Problem: rocket
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  78.904 ms | iters: 23    | obj: -1.012833e+00 (min) | CPU:  21.07 MiB
│  │  ✓ | exa_gpu  | time: 174.721 ms | iters: 24    | obj: -1.012870e+00 (min) | CPU: 12.509 MiB | GPU: 34.815 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 479.342 ms | iters: 21    | obj: -1.012820e+00 (min) | CPU:  98.57 MiB
│  │  ✓ | exa_gpu  | time: 645.685 ms | iters: 27    | obj: -1.013000e+00 (min) | CPU: 21.266 MiB | GPU: 176.399 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.190 s  | iters: 24    | obj: -1.012824e+00 (min) | CPU: 210.32 MiB
│  │  ✓ | exa_gpu  | time:   1.076 s  | iters: 27    | obj: -1.013162e+00 (min) | CPU: 30.624 MiB | GPU: 352.749 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.223 s  | iters: 21    | obj: -1.012767e+00 (min) | CPU: 392.57 MiB
│  │  ✓ | exa_gpu  | time:   1.892 s  | iters: 29    | obj: -1.013484e+00 (min) | CPU: 50.153 MiB | GPU: 711.680 MiB
│  └─
└─

┌─ Problem: space_shuttle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:   2.137 s  | iters: 110   | obj: -5.958761e-01 (min) | CPU: 164.85 MiB
│  │  ✓ | exa_gpu  | time:   2.020 s  | iters: 118   | obj: -5.959073e-01 (min) | CPU: 86.037 MiB | GPU: 185.746 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  53.657 s  | iters: 451   | obj: -5.958761e-01 (min) | CPU:   3.44 GiB
│  │  ✓ | exa_gpu  | time:   7.136 s  | iters: 116   | obj: -5.960318e-01 (min) | CPU: 127.264 MiB | GPU: 925.316 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  28.759 s  | iters: 114   | obj: -5.958761e-01 (min) | CPU:   1.62 GiB
│  │  ✓ | exa_gpu  | time:  11.703 s  | iters: 104   | obj: -5.961874e-01 (min) | CPU: 171.268 MiB | GPU:  1.769 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  66.261 s  | iters: 132   | obj: -5.958760e-01 (min) | CPU:   3.51 GiB
│  │  ✓ | exa_gpu  | time:  29.395 s  | iters: 145   | obj: -5.964987e-01 (min) | CPU: 307.333 MiB | GPU:  3.800 GiB
│  └─
└─

┌─ Problem: steering
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  75.630 ms | iters: 14    | obj: 5.545709e-01  (min) | CPU:  11.37 MiB
│  │  ✓ | exa_gpu  | time: 131.640 ms | iters: 11    | obj: 5.545709e-01  (min) | CPU:  8.181 MiB | GPU: 23.636 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 544.788 ms | iters: 14    | obj: 5.545709e-01  (min) | CPU:  54.72 MiB
│  │  ✓ | exa_gpu  | time: 479.458 ms | iters: 12    | obj: 5.545705e-01  (min) | CPU: 13.628 MiB | GPU: 118.770 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.197 s  | iters: 15    | obj: 5.545709e-01  (min) | CPU: 111.75 MiB
│  │  ✓ | exa_gpu  | time: 893.465 ms | iters: 12    | obj: 5.545706e-01  (min) | CPU: 18.395 MiB | GPU: 237.352 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.567 s  | iters: 15    | obj: 5.545709e-01  (min) | CPU: 222.96 MiB
│  │  ✓ | exa_gpu  | time:   1.666 s  | iters: 13    | obj: 5.545694e-01  (min) | CPU: 31.252 MiB | GPU: 477.246 MiB
│  └─
└─

┌─ Problem: vanderpol
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  13.949 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:   5.41 MiB
│  │  ✓ | exa_gpu  | time:  57.441 ms | iters: 8     | obj: 1.047785e+00  (min) | CPU:  5.187 MiB | GPU: 13.727 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  90.208 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  25.29 MiB
│  │  ✓ | exa_gpu  | time:  80.451 ms | iters: 7     | obj: 1.047710e+00  (min) | CPU:  9.707 MiB | GPU: 68.353 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 203.157 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  50.14 MiB
│  │  ✓ | exa_gpu  | time:  95.827 ms | iters: 8     | obj: 1.047590e+00  (min) | CPU: 13.363 MiB | GPU: 137.229 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 475.441 ms | iters: 5     | obj: 1.047807e+00  (min) | CPU: 102.12 MiB
│  │  ✓ | exa_gpu  | time: 147.936 ms | iters: 7     | obj: 1.047420e+00  (min) | CPU: 21.650 MiB | GPU: 273.360 MiB
│  └─
└─

┌─ Problem: brachistochrone
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  78.617 ms | iters: 23    | obj: 1.802932e+00  (min) | CPU:  12.69 MiB
│  │  ✓ | exa_gpu  | time: 161.781 ms | iters: 20    | obj: 1.802931e+00  (min) | CPU: 11.205 MiB | GPU: 23.607 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 688.369 ms | iters: 26    | obj: 1.802932e+00  (min) | CPU:  64.92 MiB
│  │  ✓ | exa_gpu  | time:   1.834 s  | iters: 79    | obj: 1.802923e+00  (min) | CPU: 38.189 MiB | GPU: 151.987 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.670 s  | iters: 31    | obj: 1.802935e+00  (min) | CPU: 141.30 MiB
│  │  ✓ | exa_gpu  | time:   1.135 s  | iters: 26    | obj: 1.802923e+00  (min) | CPU: 24.237 MiB | GPU: 242.057 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.798 s  | iters: 26    | obj: 1.802934e+00  (min) | CPU: 257.80 MiB
│  │  ✓ | exa_gpu  | time:   1.690 s  | iters: 21    | obj: 1.802914e+00  (min) | CPU: 33.815 MiB | GPU: 473.430 MiB
│  └─
└─

┌─ Problem: balanced_field
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 129.901 ms | iters: 25    | obj: 7.710078e+02  (min) | CPU:  26.53 MiB
│  │  ✓ | exa_gpu  | time: 289.063 ms | iters: 30    | obj: 7.709957e+02  (min) | CPU: 22.780 MiB | GPU: 54.850 MiB
│  │
│  │  N = 5000
│  │  ✗ | exa      | time:  31.580 s  | iters: 1000  | obj: 8.835924e+02  (min) | CPU:   1.99 GiB
│  │  ✓ | exa_gpu  | time:   1.524 s  | iters: 40    | obj: 7.709473e+02  (min) | CPU: 39.904 MiB | GPU: 282.896 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   4.481 s  | iters: 52    | obj: 7.710078e+02  (min) | CPU: 378.73 MiB
│  │  ✓ | exa_gpu  | time:   2.227 s  | iters: 36    | obj: 7.708868e+02  (min) | CPU: 53.616 MiB | GPU: 558.280 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   9.379 s  | iters: 50    | obj: 7.710079e+02  (min) | CPU: 719.05 MiB
│  │  ✓ | exa_gpu  | time:   5.375 s  | iters: 49    | obj: 7.707661e+02  (min) | CPU: 96.038 MiB | GPU:  1.134 GiB
│  └─
└─

┌─ Problem: bryson_denham
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  34.745 ms | iters: 20    | obj: 4.000009e+00  (min) | CPU:   6.72 MiB
│  │  ✓ | exa_gpu  | time: 518.799 ms | iters: 99    | obj: 3.999729e+00  (min) | CPU: 34.144 MiB | GPU: 15.870 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 881.260 ms | iters: 86    | obj: 4.000002e+00  (min) | CPU:  87.26 MiB
│  │  ✓ | exa_gpu  | time: 313.598 ms | iters: 70    | obj: 3.998618e+00  (min) | CPU: 26.107 MiB | GPU: 68.138 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   3.125 s  | iters: 158   | obj: 4.000004e+00  (min) | CPU: 294.86 MiB
│  │  ✓ | exa_gpu  | time: 342.614 ms | iters: 63    | obj: 3.997237e+00  (min) | CPU: 27.557 MiB | GPU: 131.014 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  14.172 s  | iters: 361   | obj: 4.000008e+00  (min) | CPU:   1.24 GiB
│  │  ✓ | exa_gpu  | time:   1.613 s  | iters: 293   | obj: 3.994479e+00  (min) | CPU: 112.981 MiB | GPU: 610.002 MiB
│  └─
└─

┌─ Problem: mountain_car
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 206.963 ms | iters: 71    | obj: 1.023686e+02  (min) | CPU:  36.51 MiB
│  │  ✓ | exa_gpu  | time:   1.124 s  | iters: 184   | obj: 1.023511e+02  (min) | CPU: 77.396 MiB | GPU: 36.856 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   2.269 s  | iters: 141   | obj: 1.023676e+02  (min) | CPU: 338.09 MiB
│  │  ✗ | exa_gpu  | time:  23.338 s  | iters: 1000  | obj: 1.136136e+02  (min) | CPU: 387.983 MiB | GPU: 662.096 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  10.889 s  | iters: 402   | obj: 1.023676e+02  (min) | CPU:   1.67 GiB
│  │  ✓ | exa_gpu  | time:   5.706 s  | iters: 166   | obj: 1.021974e+02  (min) | CPU: 83.368 MiB | GPU: 346.825 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  11.079 s  | iters: 188   | obj: 1.023676e+02  (min) | CPU:   1.63 GiB
│  │  ✓ | exa_gpu  | time:  22.810 s  | iters: 446   | obj: 1.020270e+02  (min) | CPU: 209.499 MiB | GPU:  1.264 GiB
│  └─
└─