Core benchmark: beam

This page presents benchmark results for the beam 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
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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: `beam`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	19.904	16	8.891335	min
✓	200	`adnlp`	`madnlp`	17.487	21	8.891335	min
✓	200	`exa`	`ipopt`	15.249	16	8.891335	min
✓	200	`exa`	`madnlp`	12.410	21	8.891335	min
✓	200	`jump`	`ipopt`	15.118	16	8.891335	min
✓	200	`jump`	`madnlp`	11.976	21	8.891335	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	47.187	18	8.889282	min
✓	500	`adnlp`	`madnlp`	34.664	18	8.889282	min
✓	500	`exa`	`ipopt`	35.287	18	8.889282	min
✓	500	`exa`	`madnlp`	23.990	18	8.889282	min
✓	500	`jump`	`ipopt`	36.150	18	8.889282	min
✓	500	`jump`	`madnlp`	22.318	18	8.889282	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	152.334	33	8.888988	min
✓	1000	`adnlp`	`madnlp`	94.095	26	8.888987	min
✓	1000	`exa`	`ipopt`	114.306	33	8.888987	min
✓	1000	`exa`	`madnlp`	68.506	28	8.888987	min
✓	1000	`jump`	`ipopt`	106.717	30	8.888987	min
✓	1000	`jump`	`madnlp`	66.161	28	8.888987	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	320.230	34	8.888913	min
✓	2000	`adnlp`	`madnlp`	324.210	40	8.888914	min
✓	2000	`exa`	`ipopt`	198.647	29	8.888915	min	✓
✓	2000	`exa`	`madnlp`	214.587	37	8.888913	min
✓	2000	`jump`	`ipopt`	218.396	32	8.888914	min
✓	2000	`jump`	`madnlp`	205.254	39	8.888914	min

ℹ️ Log

Benchmarks results:

┌─ Problem: beam
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  15.118 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:  16.38 KiB
│  │  ✓ | adnlp    | time:  19.904 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:   2.37 MiB
│  │  ✓ | exa      | time:  15.249 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:  72.48 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  36.150 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:  18.41 KiB
│  │  ✓ | adnlp    | time:  47.187 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   6.47 MiB
│  │  ✓ | exa      | time:  35.287 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU: 137.61 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 106.717 ms | iters: 30    | obj: 8.888987e+00  (min) | CPU:  28.56 KiB
│  │  ✓ | adnlp    | time: 152.334 ms | iters: 33    | obj: 8.888988e+00  (min) | CPU:  22.54 MiB
│  │  ✓ | exa      | time: 114.306 ms | iters: 33    | obj: 8.888987e+00  (min) | CPU: 258.77 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 218.396 ms | iters: 32    | obj: 8.888914e+00  (min) | CPU:  30.25 KiB
│  │  ✓ | adnlp    | time: 320.230 ms | iters: 34    | obj: 8.888913e+00  (min) | CPU:  46.25 MiB
│  │  ✓ | exa      | time: 198.647 ms | iters: 29    | obj: 8.888915e+00  (min) | CPU: 465.58 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  11.976 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   2.16 MiB
│  │  ✓ | adnlp    | time:  17.487 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   4.91 MiB
│  │  ✓ | exa      | time:  12.410 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   2.07 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  22.318 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   4.22 MiB
│  │  ✓ | adnlp    | time:  34.664 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:  10.13 MiB
│  │  ✓ | exa      | time:  23.990 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   4.06 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  66.161 ms | iters: 28    | obj: 8.888987e+00  (min) | CPU:  10.25 MiB
│  │  ✓ | adnlp    | time:  94.095 ms | iters: 26    | obj: 8.888987e+00  (min) | CPU:  26.56 MiB
│  │  ✓ | exa      | time:  68.506 ms | iters: 28    | obj: 8.888987e+00  (min) | CPU:   9.78 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 205.254 ms | iters: 39    | obj: 8.888914e+00  (min) | CPU:  24.93 MiB
│  │  ✓ | adnlp    | time: 324.210 ms | iters: 40    | obj: 8.888914e+00  (min) | CPU:  76.33 MiB
│  │  ✓ | exa      | time: 214.587 ms | iters: 37    | obj: 8.888913e+00  (min) | CPU:  22.69 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
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  [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
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  [82ae8749] StatsAPI v1.7.1
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  [892a3eda] StringManipulation v0.4.1
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  [a759f4b9] TimerOutputs v0.5.29
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  [d7ed1dd3] MUMPS_seq_jll v500.800.100+0
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⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.8.2+2
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⌅ [319450e9] SPRAL_jll v2025.5.20+0
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⌅ [02c8fc9c] XML2_jll v2.13.9+0
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  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
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  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
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  [4607b0f0] SuiteSparse
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  [8dfed614] Test v1.11.0
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  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+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 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: `beam`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	24.078	16	8.891335	min
✓	200	`adnlp`	`madnlp`	21.014	21	8.891335	min
✓	200	`exa`	`ipopt`	17.596	16	8.891335	min
✓	200	`exa`	`madnlp`	14.291	21	8.891335	min
✓	200	`jump`	`ipopt`	17.885	16	8.891335	min
✓	200	`jump`	`madnlp`	14.288	21	8.891335	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	54.821	18	8.889282	min
✓	500	`adnlp`	`madnlp`	41.023	18	8.889282	min
✓	500	`exa`	`ipopt`	39.561	18	8.889282	min
✓	500	`exa`	`madnlp`	27.279	18	8.889282	min
✓	500	`jump`	`ipopt`	40.744	18	8.889282	min
✓	500	`jump`	`madnlp`	27.241	18	8.889282	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	177.949	33	8.888988	min
✓	1000	`adnlp`	`madnlp`	120.920	28	8.888987	min
✓	1000	`exa`	`ipopt`	147.827	35	8.888987	min
✓	1000	`exa`	`madnlp`	71.883	26	8.888987	min
✓	1000	`jump`	`ipopt`	119.864	30	8.888987	min
✓	1000	`jump`	`madnlp`	71.061	26	8.888987	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	408.484	34	8.888913	min
✓	2000	`adnlp`	`madnlp`	391.468	40	8.888914	min
✓	2000	`exa`	`ipopt`	241.900	28	8.888915	min
✓	2000	`exa`	`madnlp`	248.128	37	8.888914	min
✓	2000	`jump`	`ipopt`	254.991	32	8.888914	min
✓	2000	`jump`	`madnlp`	227.536	38	8.888914	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	2559.959	60	8.888894	min
✓	5000	`adnlp`	`madnlp`	2421.147	80	8.888895	min
✓	5000	`exa`	`ipopt`	1316.535	52	8.888895	min
✓	5000	`exa`	`madnlp`	1206.713	79	8.888895	min
✓	5000	`jump`	`ipopt`	1355.778	53	8.888895	min
✓	5000	`jump`	`madnlp`	1129.496	80	8.888895	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: beam
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  17.885 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:  16.38 KiB
│  │  ✓ | adnlp    | time:  24.078 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:   2.37 MiB
│  │  ✓ | exa      | time:  17.596 ms | iters: 16    | obj: 8.891335e+00  (min) | CPU:  72.48 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  40.744 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:  18.41 KiB
│  │  ✓ | adnlp    | time:  54.821 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   6.47 MiB
│  │  ✓ | exa      | time:  39.561 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU: 137.61 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 119.864 ms | iters: 30    | obj: 8.888987e+00  (min) | CPU:  28.56 KiB
│  │  ✓ | adnlp    | time: 177.949 ms | iters: 33    | obj: 8.888988e+00  (min) | CPU:  22.54 MiB
│  │  ✓ | exa      | time: 147.827 ms | iters: 35    | obj: 8.888987e+00  (min) | CPU: 260.83 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 254.991 ms | iters: 32    | obj: 8.888914e+00  (min) | CPU:  30.25 KiB
│  │  ✓ | adnlp    | time: 408.484 ms | iters: 34    | obj: 8.888913e+00  (min) | CPU:  46.25 MiB
│  │  ✓ | exa      | time: 241.900 ms | iters: 28    | obj: 8.888915e+00  (min) | CPU: 464.55 KiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   1.356 s  | iters: 53    | obj: 8.888895e+00  (min) | CPU:  47.97 KiB
│  │  ✓ | adnlp    | time:   2.560 s  | iters: 60    | obj: 8.888894e+00  (min) | CPU: 198.84 MiB
│  │  ✓ | exa      | time:   1.317 s  | iters: 52    | obj: 8.888895e+00  (min) | CPU:   1.10 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  14.288 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   2.16 MiB
│  │  ✓ | adnlp    | time:  21.014 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   4.91 MiB
│  │  ✓ | exa      | time:  14.291 ms | iters: 21    | obj: 8.891335e+00  (min) | CPU:   2.07 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  27.241 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   4.22 MiB
│  │  ✓ | adnlp    | time:  41.023 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:  10.13 MiB
│  │  ✓ | exa      | time:  27.279 ms | iters: 18    | obj: 8.889282e+00  (min) | CPU:   4.06 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  71.061 ms | iters: 26    | obj: 8.888987e+00  (min) | CPU:   9.78 MiB
│  │  ✓ | adnlp    | time: 120.920 ms | iters: 28    | obj: 8.888987e+00  (min) | CPU:  28.42 MiB
│  │  ✓ | exa      | time:  71.883 ms | iters: 26    | obj: 8.888987e+00  (min) | CPU:   9.30 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 227.536 ms | iters: 38    | obj: 8.888914e+00  (min) | CPU:  24.51 MiB
│  │  ✓ | adnlp    | time: 391.468 ms | iters: 40    | obj: 8.888914e+00  (min) | CPU:  76.33 MiB
│  │  ✓ | exa      | time: 248.128 ms | iters: 37    | obj: 8.888914e+00  (min) | CPU:  22.63 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   1.129 s  | iters: 80    | obj: 8.888895e+00  (min) | CPU: 103.92 MiB
│  │  ✓ | adnlp    | time:   2.421 s  | iters: 80    | obj: 8.888895e+00  (min) | CPU: 359.44 MiB
│  │  ✓ | exa      | time:   1.207 s  | iters: 79    | obj: 8.888895e+00  (min) | CPU:  99.12 MiB
│  └─
└─

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
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  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
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  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
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  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
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  [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
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  [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
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  [ae029012] Requires v1.3.1
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  [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
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  [90137ffa] StaticArrays v1.9.15
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⌅ [30392449] Pixman_jll v0.44.2+0
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  [a44049a8] Vulkan_Loader_jll v1.3.243+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: `beam`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	60.927	22	8.889006	min	✓
✓	1000	`exa_gpu`	`madnlp`	153.209	25	8.827707	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	315.917	17	8.888990	min
✓	5000	`exa_gpu`	`madnlp`	203.646	31	8.586481	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	715.055	18	8.889088	min
✓	10000	`exa_gpu`	`madnlp`	211.004	22	8.291850	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	1211.744	13	8.889279	min
✓	20000	`exa_gpu`	`madnlp`	295.685	20	7.725138	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: beam
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  60.927 ms | iters: 22    | obj: 8.889006e+00  (min) | CPU:   8.45 MiB
│  │  ✓ | exa_gpu  | time: 153.209 ms | iters: 25    | obj: 8.827707e+00  (min) | CPU:  9.171 MiB | GPU: 11.901 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 315.917 ms | iters: 17    | obj: 8.888990e+00  (min) | CPU:  34.86 MiB
│  │  ✓ | exa_gpu  | time: 203.646 ms | iters: 31    | obj: 8.586481e+00  (min) | CPU: 12.994 MiB | GPU: 61.717 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 715.055 ms | iters: 18    | obj: 8.889088e+00  (min) | CPU:  71.26 MiB
│  │  ✓ | exa_gpu  | time: 211.004 ms | iters: 22    | obj: 8.291850e+00  (min) | CPU: 12.801 MiB | GPU: 116.519 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   1.212 s  | iters: 13    | obj: 8.889279e+00  (min) | CPU: 121.36 MiB
│  │  ✓ | exa_gpu  | time: 295.685 ms | iters: 20    | obj: 7.725138e+00  (min) | CPU: 17.206 MiB | GPU: 229.899 MiB
│  └─
└─