Core GPU Benchmark

Julia Version 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 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-18.1.7 (ORCJIT, sapphirerapids)
  GC: Built with stock GC
Threads: 1 default, 1 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 v5.10.1
  [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 v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [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 v1.12.1
  [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 To see why use `status --outdated`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 `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
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  [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 v0.7.3-beta
  [052768ef] CUDA v5.10.1
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.7
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  [b6b21f68] Ipopt v1.14.1
  [92d709cd] IrrationalConstants v0.2.6
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  [63c18a36] KernelAbstractions v0.9.40
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  [929cbde3] LLVM v9.4.6
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  [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
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  [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
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  [4d8831e6] OpenSSL v1.6.1
⌅ [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
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  [2dfb63ee] PooledArrays v1.4.3
  [aea7be01] PrecompileTools v1.3.3
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  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
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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`

Benchmarks results:

┌─ Problem: balanced_field
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 125.908 ms | iters: 25    | obj: 7.710078e+02  (min) | CPU:  26.22 MiB
│  │  ✓ | exa_gpu  | time: 390.709 ms | iters: 30    | obj: 7.709957e+02  (min) | CPU: 17.762 MiB | GPU: 54.845 MiB
│  │
│  │  N = 5000
│  │  ✗ | exa      | time:  28.604 s  | iters: 1000  | obj: 8.835924e+02  (min) | CPU:   1.99 GiB
│  │  ✓ | exa_gpu  | time:   1.765 s  | iters: 45    | obj: 7.709473e+02  (min) | CPU: 37.512 MiB | GPU: 287.060 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   4.428 s  | iters: 52    | obj: 7.710078e+02  (min) | CPU: 378.43 MiB
│  │  ✓ | exa_gpu  | time:   3.543 s  | iters: 47    | obj: 7.708868e+02  (min) | CPU: 54.327 MiB | GPU: 578.047 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   9.331 s  | iters: 50    | obj: 7.710079e+02  (min) | CPU: 718.75 MiB
│  │  ✓ | exa_gpu  | time:   6.798 s  | iters: 45    | obj: 7.707661e+02  (min) | CPU: 83.880 MiB | GPU:  1.120 GiB
│  └─
└─

┌─ Problem: beam
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  42.732 ms | iters: 26    | obj: 8.888914e+00  (min) | CPU:   8.58 MiB
│  │  ✓ | exa_gpu  | time: 212.845 ms | iters: 48    | obj: 8.888302e+00  (min) | CPU: 12.603 MiB | GPU: 12.066 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 711.511 ms | iters: 79    | obj: 8.888892e+00  (min) | CPU:  96.73 MiB
│  │  ✓ | exa_gpu  | time: 612.023 ms | iters: 138   | obj: 8.885839e+00  (min) | CPU: 36.286 MiB | GPU: 94.366 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   3.019 s  | iters: 175   | obj: 8.888893e+00  (min) | CPU: 391.26 MiB
│  │  ✓ | exa_gpu  | time:   1.568 s  | iters: 278   | obj: 8.882791e+00  (min) | CPU: 67.082 MiB | GPU: 294.516 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   7.444 s  | iters: 189   | obj: 8.888898e+00  (min) | CPU: 841.22 MiB
│  │  ✓ | exa_gpu  | time:   2.416 s  | iters: 380   | obj: 8.876698e+00  (min) | CPU: 95.541 MiB | GPU: 742.618 MiB
│  └─
└─

┌─ Problem: brachistochrone
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  75.649 ms | iters: 23    | obj: 1.802932e+00  (min) | CPU:  12.38 MiB
│  │  ✓ | exa_gpu  | time: 216.800 ms | iters: 20    | obj: 1.802931e+00  (min) | CPU:  8.593 MiB | GPU: 23.605 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 658.702 ms | iters: 26    | obj: 1.802932e+00  (min) | CPU:  64.61 MiB
│  │  ✓ | exa_gpu  | time:   1.366 s  | iters: 41    | obj: 1.802923e+00  (min) | CPU: 19.515 MiB | GPU: 132.175 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.689 s  | iters: 31    | obj: 1.802935e+00  (min) | CPU: 140.99 MiB
│  │  ✓ | exa_gpu  | time:   1.405 s  | iters: 26    | obj: 1.802923e+00  (min) | CPU: 20.999 MiB | GPU: 242.052 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.716 s  | iters: 26    | obj: 1.802934e+00  (min) | CPU: 257.49 MiB
│  │  ✓ | exa_gpu  | time:   1.671 s  | iters: 21    | obj: 1.802914e+00  (min) | CPU: 31.247 MiB | GPU: 473.443 MiB
│  └─
└─

┌─ Problem: bryson_denham
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  32.993 ms | iters: 20    | obj: 4.000009e+00  (min) | CPU:   6.41 MiB
│  │  ✓ | exa_gpu  | time: 345.361 ms | iters: 100   | obj: 3.999729e+00  (min) | CPU: 25.446 MiB | GPU: 15.949 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 761.245 ms | iters: 86    | obj: 4.000002e+00  (min) | CPU:  86.98 MiB
│  │  ✓ | exa_gpu  | time: 328.077 ms | iters: 78    | obj: 3.998618e+00  (min) | CPU: 21.569 MiB | GPU: 71.162 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.693 s  | iters: 158   | obj: 4.000004e+00  (min) | CPU: 294.61 MiB
│  │  ✓ | exa_gpu  | time: 464.480 ms | iters: 83    | obj: 3.997237e+00  (min) | CPU: 27.555 MiB | GPU: 146.370 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  12.111 s  | iters: 361   | obj: 4.000008e+00  (min) | CPU:   1.24 GiB
│  │  ✓ | exa_gpu  | time: 862.183 ms | iters: 128   | obj: 3.994477e+00  (min) | CPU: 44.041 MiB | GPU: 360.676 MiB
│  └─
└─

┌─ Problem: chain
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  36.017 ms | iters: 14    | obj: 5.068480e+00  (min) | CPU:   6.42 MiB
│  │  ✓ | exa_gpu  | time: 101.377 ms | iters: 15    | obj: 5.068452e+00  (min) | CPU:  6.011 MiB | GPU: 14.327 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 292.398 ms | iters: 13    | obj: 5.068480e+00  (min) | CPU:  30.57 MiB
│  │  ✓ | exa_gpu  | time: 140.849 ms | iters: 16    | obj: 5.068339e+00  (min) | CPU:  8.992 MiB | GPU: 72.020 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 597.481 ms | iters: 13    | obj: 5.068480e+00  (min) | CPU:  60.94 MiB
│  │  ✓ | exa_gpu  | time:   4.531 s  | iters: 379   | obj: 5.068201e+00  (min) | CPU: 175.949 MiB | GPU: 492.775 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.068 s  | iters: 14    | obj: 5.068480e+00  (min) | CPU: 124.75 MiB
│  │  ✓ | exa_gpu  | time: 234.628 ms | iters: 15    | obj: 5.067922e+00  (min) | CPU: 18.258 MiB | GPU: 286.065 MiB
│  └─
└─

┌─ Problem: dielectrophoretic_particle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  32.094 ms | iters: 16    | obj: 7.811315e+00  (min) | CPU:   8.40 MiB
│  │  ✓ | exa_gpu  | time: 133.867 ms | iters: 15    | obj: 7.811169e+00  (min) | CPU:  6.009 MiB | GPU: 15.812 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 230.248 ms | iters: 17    | obj: 7.811315e+00  (min) | CPU:  42.23 MiB
│  │  ✓ | exa_gpu  | time: 377.406 ms | iters: 16    | obj: 7.810584e+00  (min) | CPU:  9.663 MiB | GPU: 79.388 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 476.921 ms | iters: 17    | obj: 7.811331e+00  (min) | CPU:  84.09 MiB
│  │  ✓ | exa_gpu  | time: 925.237 ms | iters: 22    | obj: 7.809900e+00  (min) | CPU: 15.639 MiB | GPU: 163.298 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 997.569 ms | iters: 18    | obj: 7.811350e+00  (min) | CPU: 172.08 MiB
│  │  ✓ | exa_gpu  | time:   1.323 s  | iters: 18    | obj: 7.808404e+00  (min) | CPU: 22.991 MiB | GPU: 320.446 MiB
│  └─
└─

┌─ Problem: double_oscillator
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  23.141 ms | iters: 6     | obj: 9.110011e-04  (min) | CPU:  10.33 MiB
│  │  ✓ | exa_gpu  | time:  68.848 ms | iters: 6     | obj: 9.106227e-04  (min) | CPU:  4.810 MiB | GPU: 29.597 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 286.415 ms | iters: 6     | obj: 9.110335e-04  (min) | CPU:  50.99 MiB
│  │  ✓ | exa_gpu  | time:  99.414 ms | iters: 6     | obj: 9.091472e-04  (min) | CPU: 12.096 MiB | GPU: 148.003 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 602.634 ms | iters: 6     | obj: 9.110345e-04  (min) | CPU: 101.84 MiB
│  │  ✓ | exa_gpu  | time: 138.835 ms | iters: 6     | obj: 9.072690e-04  (min) | CPU: 19.266 MiB | GPU: 295.850 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   1.403 s  | iters: 6     | obj: 9.110348e-04  (min) | CPU: 203.53 MiB
│  │  ✓ | exa_gpu  | time: 237.410 ms | iters: 6     | obj: 9.035309e-04  (min) | CPU: 35.246 MiB | GPU: 591.574 MiB
│  └─
└─

┌─ Problem: ducted_fan
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 908.455 ms | iters: 68    | obj: 1.831621e+03  (min) | CPU:  58.13 MiB
│  │  ✓ | exa_gpu  | time:   1.175 s  | iters: 65    | obj: 1.831594e+03  (min) | CPU: 29.924 MiB | GPU: 63.191 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  19.159 s  | iters: 331   | obj: 1.831610e+03  (min) | CPU:   1.34 GiB
│  │  ✓ | exa_gpu  | time:   7.298 s  | iters: 109   | obj: 1.831477e+03  (min) | CPU: 68.298 MiB | GPU: 369.067 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  22.893 s  | iters: 156   | obj: 1.831610e+03  (min) | CPU:   1.76 GiB
│  │  ✓ | exa_gpu  | time:  14.550 s  | iters: 130   | obj: 1.831344e+03  (min) | CPU: 93.490 MiB | GPU: 785.210 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  61.641 s  | iters: 204   | obj: 1.831610e+03  (min) | CPU:   3.99 GiB
│  │  ✓ | exa_gpu  | time:  19.398 s  | iters: 99    | obj: 1.831081e+03  (min) | CPU: 97.848 MiB | GPU:  1.381 GiB
│  └─
└─

┌─ Problem: electric_vehicle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  10.375 ms | iters: 4     | obj: 1.228583e+03  (min) | CPU:   4.63 MiB
│  │  ✓ | exa_gpu  | time:  76.712 ms | iters: 11    | obj: 1.228577e+03  (min) | CPU:  4.878 MiB | GPU: 13.152 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 114.105 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  23.22 MiB
│  │  ✓ | exa_gpu  | time: 101.188 ms | iters: 11    | obj: 1.228551e+03  (min) | CPU:  8.255 MiB | GPU: 65.727 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 241.446 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  46.31 MiB
│  │  ✓ | exa_gpu  | time: 110.253 ms | iters: 10    | obj: 1.228521e+03  (min) | CPU: 11.154 MiB | GPU: 130.827 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 513.994 ms | iters: 5     | obj: 1.228580e+03  (min) | CPU:  92.48 MiB
│  │  ✓ | exa_gpu  | time: 155.956 ms | iters: 10    | obj: 1.228463e+03  (min) | CPU: 18.293 MiB | GPU: 261.633 MiB
│  └─
└─

┌─ Problem: glider
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 845.956 ms | iters: 102   | obj: -1.247985e+03 (min) | CPU:  62.56 MiB
│  │  ✓ | exa_gpu  | time: 520.614 ms | iters: 29    | obj: -1.247986e+03 (min) | CPU: 29.446 MiB | GPU: 55.065 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 749.463 ms | iters: 16    | obj: -1.247987e+03 (min) | CPU: 122.33 MiB
│  │  ✓ | exa_gpu  | time: 914.104 ms | iters: 21    | obj: -1.247990e+03 (min) | CPU: 35.738 MiB | GPU: 267.906 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.568 s  | iters: 16    | obj: -1.247988e+03 (min) | CPU: 244.26 MiB
│  │  ✓ | exa_gpu  | time:   1.492 s  | iters: 22    | obj: -1.247993e+03 (min) | CPU: 51.865 MiB | GPU: 536.938 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   3.759 s  | iters: 17    | obj: -1.247988e+03 (min) | CPU: 495.91 MiB
│  │  ✓ | exa_gpu  | time:   2.777 s  | iters: 19    | obj: -1.247998e+03 (min) | CPU: 84.240 MiB | GPU:  1.038 GiB
│  └─
└─

┌─ Problem: insurance
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:   3.396 s  | iters: 313   | obj: -2.058233e+00 (min) | CPU: 282.10 MiB
│  │  ✓ | exa_gpu  | time:   3.677 s  | iters: 496   | obj: -2.058242e+00 (min) | CPU: 174.693 MiB | GPU: 197.783 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  31.798 s  | iters: 757   | obj: -2.059098e+00 (min) | CPU:   3.07 GiB
│  │  ✓ | exa_gpu  | time:   6.373 s  | iters: 429   | obj: -2.059144e+00 (min) | CPU: 175.392 MiB | GPU: 875.526 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  67.209 s  | iters: 573   | obj: -2.059342e+00 (min) | CPU:   4.64 GiB
│  │  ✓ | exa_gpu  | time:  15.345 s  | iters: 565   | obj: -2.059436e+00 (min) | CPU: 236.291 MiB | GPU:  2.149 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 184.583 s  | iters: 705   | obj: -2.059516e+00 (min) | CPU:  11.86 GiB
│  │  ✗ | exa_gpu  | time:  50.955 s  | iters: 1000  | obj: -2.059700e+00 (min) | CPU: 718.409 MiB | GPU:  7.128 GiB
│  └─
└─

┌─ Problem: jackson
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  57.447 ms | iters: 23    | obj: -1.918150e-01 (min) | CPU:  20.57 MiB
│  │  ✓ | exa_gpu  | time: 114.304 ms | iters: 22    | obj: -1.918374e-01 (min) | CPU:  8.029 MiB | GPU: 26.361 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 392.869 ms | iters: 21    | obj: -1.918128e-01 (min) | CPU:  96.60 MiB
│  │  ✓ | exa_gpu  | time: 178.371 ms | iters: 25    | obj: -1.919247e-01 (min) | CPU: 14.565 MiB | GPU: 134.152 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 809.497 ms | iters: 21    | obj: -1.918111e-01 (min) | CPU: 192.94 MiB
│  │  ✓ | exa_gpu  | time: 229.836 ms | iters: 24    | obj: -1.920350e-01 (min) | CPU: 21.165 MiB | GPU: 266.616 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   1.651 s  | iters: 20    | obj: -1.918079e-01 (min) | CPU: 375.26 MiB
│  │  ✓ | exa_gpu  | time: 343.287 ms | iters: 21    | obj: -1.922558e-01 (min) | CPU: 33.895 MiB | GPU: 523.312 MiB
│  └─
└─

┌─ Problem: mountain_car
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 196.025 ms | iters: 71    | obj: 1.023686e+02  (min) | CPU:  36.18 MiB
│  │  ✓ | exa_gpu  | time:   1.858 s  | iters: 215   | obj: 1.023511e+02  (min) | CPU: 71.989 MiB | GPU: 40.504 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.891 s  | iters: 141   | obj: 1.023676e+02  (min) | CPU: 337.62 MiB
│  │  ✗ | exa_gpu  | time:  28.378 s  | iters: 1000  | obj: 1.052239e+02  (min) | CPU: 296.607 MiB | GPU: 662.716 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   9.188 s  | iters: 402   | obj: 1.023676e+02  (min) | CPU:   1.67 GiB
│  │  ✓ | exa_gpu  | time:   7.174 s  | iters: 166   | obj: 1.021974e+02  (min) | CPU: 65.857 MiB | GPU: 346.866 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   9.315 s  | iters: 188   | obj: 1.023676e+02  (min) | CPU:   1.63 GiB
│  │  ✓ | exa_gpu  | time:  22.890 s  | iters: 476   | obj: 1.020269e+02  (min) | CPU: 164.832 MiB | GPU:  1.333 GiB
│  └─
└─

┌─ Problem: robbins
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 180.261 ms | iters: 44    | obj: 1.943317e+01  (min) | CPU:  14.02 MiB
│  │  ✓ | exa_gpu  | time: 269.726 ms | iters: 44    | obj: 1.943298e+01  (min) | CPU: 13.448 MiB | GPU: 18.338 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.214 s  | iters: 75    | obj: 1.943184e+01  (min) | CPU: 100.45 MiB
│  │  ✓ | exa_gpu  | time: 269.358 ms | iters: 49    | obj: 1.943093e+01  (min) | CPU: 17.776 MiB | GPU: 94.103 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.114 s  | iters: 63    | obj: 1.943181e+01  (min) | CPU: 176.24 MiB
│  │  ✓ | exa_gpu  | time: 556.052 ms | iters: 96    | obj: 1.942999e+01  (min) | CPU: 34.292 MiB | GPU: 237.016 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   5.656 s  | iters: 71    | obj: 1.943181e+01  (min) | CPU: 386.61 MiB
│  │  ✓ | exa_gpu  | time: 941.567 ms | iters: 132   | obj: 1.942818e+01  (min) | CPU: 51.031 MiB | GPU: 547.984 MiB
│  └─
└─

┌─ Problem: robot
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 309.250 ms | iters: 23    | obj: 9.140917e+00  (min) | CPU:  37.62 MiB
│  │  ✓ | exa_gpu  | time: 573.565 ms | iters: 29    | obj: 9.140745e+00  (min) | CPU: 15.131 MiB | GPU: 58.809 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   4.080 s  | iters: 50    | obj: 9.140949e+00  (min) | CPU: 311.47 MiB
│  │  ✓ | exa_gpu  | time:   3.455 s  | iters: 55    | obj: 9.140131e+00  (min) | CPU: 37.561 MiB | GPU: 337.889 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   5.684 s  | iters: 34    | obj: 9.140939e+00  (min) | CPU: 464.72 MiB
│  │  ✓ | exa_gpu  | time:   5.079 s  | iters: 54    | obj: 9.139277e+00  (min) | CPU: 48.524 MiB | GPU: 658.224 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  26.214 s  | iters: 41    | obj: 9.140966e+00  (min) | CPU:   1.12 GiB
│  │  ✓ | exa_gpu  | time:   5.743 s  | iters: 31    | obj: 9.137650e+00  (min) | CPU: 67.790 MiB | GPU:  1.157 GiB
│  └─
└─

┌─ Problem: rocket
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  76.248 ms | iters: 23    | obj: -1.012833e+00 (min) | CPU:  20.76 MiB
│  │  ✓ | exa_gpu  | time: 176.834 ms | iters: 24    | obj: -1.012870e+00 (min) | CPU:  9.887 MiB | GPU: 34.815 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 462.257 ms | iters: 21    | obj: -1.012820e+00 (min) | CPU:  98.26 MiB
│  │  ✓ | exa_gpu  | time: 748.508 ms | iters: 27    | obj: -1.013000e+00 (min) | CPU: 18.344 MiB | GPU: 176.402 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.044 s  | iters: 24    | obj: -1.012824e+00 (min) | CPU: 210.01 MiB
│  │  ✓ | exa_gpu  | time:   1.223 s  | iters: 27    | obj: -1.013162e+00 (min) | CPU: 27.696 MiB | GPU: 352.756 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.171 s  | iters: 21    | obj: -1.012767e+00 (min) | CPU: 392.25 MiB
│  │  ✓ | exa_gpu  | time:   2.374 s  | iters: 29    | obj: -1.013484e+00 (min) | CPU: 47.044 MiB | GPU: 711.693 MiB
│  └─
└─

┌─ Problem: space_shuttle
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:   2.073 s  | iters: 110   | obj: -5.958761e-01 (min) | CPU: 164.45 MiB
│  │  ✓ | exa_gpu  | time:   2.629 s  | iters: 118   | obj: -5.959073e-01 (min) | CPU: 74.022 MiB | GPU: 185.754 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  47.975 s  | iters: 451   | obj: -5.958761e-01 (min) | CPU:   3.44 GiB
│  │  ✓ | exa_gpu  | time:   7.039 s  | iters: 116   | obj: -5.960318e-01 (min) | CPU: 113.195 MiB | GPU: 925.357 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  27.640 s  | iters: 114   | obj: -5.958761e-01 (min) | CPU:   1.62 GiB
│  │  ✓ | exa_gpu  | time:  15.531 s  | iters: 104   | obj: -5.961874e-01 (min) | CPU: 159.619 MiB | GPU:  1.769 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  66.251 s  | iters: 132   | obj: -5.958760e-01 (min) | CPU:   3.51 GiB
│  │  ✓ | exa_gpu  | time:  29.538 s  | iters: 134   | obj: -5.964987e-01 (min) | CPU: 279.054 MiB | GPU:  3.730 GiB
│  └─
└─

┌─ Problem: steering
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  74.469 ms | iters: 14    | obj: 5.545709e-01  (min) | CPU:  11.05 MiB
│  │  ✓ | exa_gpu  | time: 177.044 ms | iters: 12    | obj: 5.545709e-01  (min) | CPU:  6.900 MiB | GPU: 23.773 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 540.844 ms | iters: 14    | obj: 5.545709e-01  (min) | CPU:  54.40 MiB
│  │  ✓ | exa_gpu  | time: 641.387 ms | iters: 13    | obj: 5.545705e-01  (min) | CPU: 11.460 MiB | GPU: 119.405 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.191 s  | iters: 15    | obj: 5.545709e-01  (min) | CPU: 111.43 MiB
│  │  ✓ | exa_gpu  | time:   1.162 s  | iters: 12    | obj: 5.545701e-01  (min) | CPU: 17.647 MiB | GPU: 237.464 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   2.566 s  | iters: 15    | obj: 5.545709e-01  (min) | CPU: 222.64 MiB
│  │  ✓ | exa_gpu  | time:   2.984 s  | iters: 18    | obj: 5.545694e-01  (min) | CPU: 31.771 MiB | GPU: 490.552 MiB
│  └─
└─

┌─ Problem: vanderpol
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  13.597 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:   5.09 MiB
│  │  ✓ | exa_gpu  | time:  55.960 ms | iters: 8     | obj: 1.047785e+00  (min) | CPU:  4.058 MiB | GPU: 13.727 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  88.773 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  24.97 MiB
│  │  ✓ | exa_gpu  | time:  86.344 ms | iters: 7     | obj: 1.047710e+00  (min) | CPU:  8.125 MiB | GPU: 68.352 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 185.402 ms | iters: 4     | obj: 1.047807e+00  (min) | CPU:  49.81 MiB
│  │  ✓ | exa_gpu  | time: 110.559 ms | iters: 8     | obj: 1.047590e+00  (min) | CPU: 12.052 MiB | GPU: 137.232 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 426.464 ms | iters: 5     | obj: 1.047807e+00  (min) | CPU: 101.80 MiB
│  │  ✓ | exa_gpu  | time: 137.807 ms | iters: 8     | obj: 1.047373e+00  (min) | CPU: 19.275 MiB | GPU: 274.344 MiB
│  └─
└─