Core benchmark: robot

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

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	119.609	19	9.141395	min
✓	200	`adnlp`	`madnlp`	157.126	25	9.141397	min
✓	200	`exa`	`ipopt`	72.825	19	9.141395	min	✓
✓	200	`exa`	`madnlp`	75.433	23	9.141397	min
✓	200	`jump`	`ipopt`	101.020	19	9.141395	min
✓	200	`jump`	`madnlp`	114.948	23	9.141397	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	363.129	22	9.140990	min
✓	500	`adnlp`	`madnlp`	508.021	29	9.140992	min
✓	500	`exa`	`ipopt`	201.961	22	9.140990	min	✓
✓	500	`exa`	`madnlp`	237.411	29	9.140992	min
✓	500	`jump`	`ipopt`	304.818	22	9.140990	min
✓	500	`jump`	`madnlp`	392.982	29	9.140992	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	1422.132	33	9.140933	min
✓	1000	`adnlp`	`madnlp`	1004.351	28	9.140939	min
✓	1000	`exa`	`ipopt`	631.095	31	9.140932	min
✓	1000	`exa`	`madnlp`	570.753	28	9.140939	min	✓
✓	1000	`jump`	`ipopt`	1261.243	35	9.140931	min
✓	1000	`jump`	`madnlp`	1004.227	28	9.140939	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	3026.293	30	9.140917	min
✗	2000	`adnlp`	`madnlp`	N/A	N/A	N/A	N/A
✓	2000	`exa`	`ipopt`	1444.187	30	9.140917	min	✓
✓	2000	`exa`	`madnlp`	2623.774	49	9.140922	min
✓	2000	`jump`	`ipopt`	2590.731	30	9.140917	min
✓	2000	`jump`	`madnlp`	16756.459	182	9.140931	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robot
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 101.020 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU:  37.98 KiB
│  │  ✓ | adnlp    | time: 119.609 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU:  13.56 MiB
│  │  ✓ | exa      | time:  72.825 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU: 181.86 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 304.818 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU:  43.56 KiB
│  │  ✓ | adnlp    | time: 363.129 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU:  38.52 MiB
│  │  ✓ | exa      | time: 201.961 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU: 374.58 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   1.261 s  | iters: 35    | obj: 9.140931e+00  (min) | CPU:  69.30 KiB
│  │  ✓ | adnlp    | time:   1.422 s  | iters: 33    | obj: 9.140933e+00  (min) | CPU: 113.19 MiB
│  │  ✓ | exa      | time: 631.095 ms | iters: 31    | obj: 9.140932e+00  (min) | CPU: 701.30 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   2.591 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU:  58.44 KiB
│  │  ✓ | adnlp    | time:   3.026 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU: 205.28 MiB
│  │  ✓ | exa      | time:   1.444 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU:   1.30 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 114.948 ms | iters: 23    | obj: 9.141397e+00  (min) | CPU:  23.90 MiB
│  │  ✓ | adnlp    | time: 157.126 ms | iters: 25    | obj: 9.141397e+00  (min) | CPU:  24.89 MiB
│  │  ✓ | exa      | time:  75.433 ms | iters: 23    | obj: 9.141397e+00  (min) | CPU:   8.24 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 392.982 ms | iters: 29    | obj: 9.140992e+00  (min) | CPU:  62.28 MiB
│  │  ✓ | adnlp    | time: 508.021 ms | iters: 29    | obj: 9.140992e+00  (min) | CPU:  70.01 MiB
│  │  ✓ | exa      | time: 237.411 ms | iters: 29    | obj: 9.140992e+00  (min) | CPU:  22.72 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   1.004 s  | iters: 28    | obj: 9.140939e+00  (min) | CPU: 125.45 MiB
│  │  ✓ | adnlp    | time:   1.004 s  | iters: 28    | obj: 9.140939e+00  (min) | CPU: 134.27 MiB
│  │  ✓ | exa      | time: 570.753 ms | iters: 28    | obj: 9.140939e+00  (min) | CPU:  43.46 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  16.756 s  | iters: 182   | obj: 9.140931e+00  (min) | CPU: 583.10 MiB
│  │  ✗ | adnlp   : ERROR: DomainError(Inf, "sincos(x) is only defined for finite x.")
│  │  ✓ | exa      | time:   2.624 s  | iters: 49    | obj: 9.140922e+00  (min) | CPU: 180.65 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
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  [14f7f29c] AMD v0.5.3
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  [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
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  [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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  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
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⌅ [30392449] Pixman_jll v0.44.2+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
  [b77e0a4c] InteractiveUtils v1.11.0
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  [b27032c2] LibCURL v0.6.4
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  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
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  [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
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  [c8ffd9c3] MbedTLS_jll v2.28.6+0
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  [05823500] OpenLibm_jll v0.8.5+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: `robot`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	142.201	19	9.141395	min
✓	200	`adnlp`	`madnlp`	181.580	23	9.141397	min
✓	200	`exa`	`ipopt`	79.687	19	9.141395	min	✓
✓	200	`exa`	`madnlp`	83.808	23	9.141397	min
✓	200	`jump`	`ipopt`	116.437	19	9.141395	min
✓	200	`jump`	`madnlp`	162.379	25	9.141397	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	443.072	22	9.140990	min
✓	500	`adnlp`	`madnlp`	896.162	30	9.140992	min
✓	500	`exa`	`ipopt`	219.928	22	9.140990	min	✓
✓	500	`exa`	`madnlp`	267.521	29	9.140992	min
✓	500	`jump`	`ipopt`	375.984	22	9.140990	min
✓	500	`jump`	`madnlp`	545.902	32	9.140992	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	2015.402	35	9.140931	min
✗	1000	`adnlp`	`madnlp`	N/A	N/A	N/A	N/A
✓	1000	`exa`	`ipopt`	705.407	31	9.140932	min
✓	1000	`exa`	`madnlp`	666.126	28	9.140939	min	✓
✓	1000	`jump`	`ipopt`	1400.050	33	9.140932	min
✓	1000	`jump`	`madnlp`	1273.656	28	9.140939	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	4813.559	30	9.140917	min
✓	2000	`adnlp`	`madnlp`	8498.111	46	9.140922	min
✓	2000	`exa`	`ipopt`	1688.362	30	9.140917	min	✓
✓	2000	`exa`	`madnlp`	3362.655	53	9.140922	min
✓	2000	`jump`	`ipopt`	3060.808	30	9.140917	min
✓	2000	`jump`	`madnlp`	4088.157	38	9.140931	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	12440.248	27	9.140946	min
✓	5000	`adnlp`	`madnlp`	14522.580	36	9.140950	min
✓	5000	`exa`	`ipopt`	5460.668	27	9.140946	min	✓
✓	5000	`exa`	`madnlp`	8545.441	45	9.140950	min
✓	5000	`jump`	`ipopt`	8140.923	27	9.140946	min
✓	5000	`jump`	`madnlp`	13759.553	45	9.140950	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robot
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 116.437 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU:  37.98 KiB
│  │  ✓ | adnlp    | time: 142.201 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU:  13.56 MiB
│  │  ✓ | exa      | time:  79.687 ms | iters: 19    | obj: 9.141395e+00  (min) | CPU: 181.86 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 375.984 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU:  43.56 KiB
│  │  ✓ | adnlp    | time: 443.072 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU:  38.52 MiB
│  │  ✓ | exa      | time: 219.928 ms | iters: 22    | obj: 9.140990e+00  (min) | CPU: 374.58 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   1.400 s  | iters: 33    | obj: 9.140932e+00  (min) | CPU:  65.58 KiB
│  │  ✓ | adnlp    | time:   2.015 s  | iters: 35    | obj: 9.140931e+00  (min) | CPU: 119.67 MiB
│  │  ✓ | exa      | time: 705.407 ms | iters: 31    | obj: 9.140932e+00  (min) | CPU: 701.30 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   3.061 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU:  58.44 KiB
│  │  ✓ | adnlp    | time:   4.814 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU: 205.28 MiB
│  │  ✓ | exa      | time:   1.688 s  | iters: 30    | obj: 9.140917e+00  (min) | CPU:   1.30 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   8.141 s  | iters: 27    | obj: 9.140946e+00  (min) | CPU:  52.86 KiB
│  │  ✓ | adnlp    | time:  12.440 s  | iters: 27    | obj: 9.140946e+00  (min) | CPU: 464.24 MiB
│  │  ✓ | exa      | time:   5.461 s  | iters: 27    | obj: 9.140946e+00  (min) | CPU:   3.15 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 162.379 ms | iters: 25    | obj: 9.141397e+00  (min) | CPU:  24.28 MiB
│  │  ✓ | adnlp    | time: 181.580 ms | iters: 23    | obj: 9.141397e+00  (min) | CPU:  23.19 MiB
│  │  ✓ | exa      | time:  83.808 ms | iters: 23    | obj: 9.141397e+00  (min) | CPU:   8.24 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 545.902 ms | iters: 32    | obj: 9.140992e+00  (min) | CPU:  63.76 MiB
│  │  ✓ | adnlp    | time: 896.162 ms | iters: 30    | obj: 9.140992e+00  (min) | CPU:  71.56 MiB
│  │  ✓ | exa      | time: 267.521 ms | iters: 29    | obj: 9.140992e+00  (min) | CPU:  22.73 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   1.274 s  | iters: 28    | obj: 9.140939e+00  (min) | CPU: 125.45 MiB
│  │  ✗ | adnlp   : ERROR: DomainError(Inf, "sincos(x) is only defined for finite x.")
│  │  ✓ | exa      | time: 666.126 ms | iters: 28    | obj: 9.140939e+00  (min) | CPU:  43.46 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   4.088 s  | iters: 38    | obj: 9.140931e+00  (min) | CPU: 268.46 MiB
│  │  ✓ | adnlp    | time:   8.498 s  | iters: 46    | obj: 9.140922e+00  (min) | CPU: 481.34 MiB
│  │  ✓ | exa      | time:   3.363 s  | iters: 53    | obj: 9.140922e+00  (min) | CPU: 189.93 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:  13.760 s  | iters: 45    | obj: 9.140950e+00  (min) | CPU: 739.11 MiB
│  │  ✓ | adnlp    | time:  14.523 s  | iters: 36    | obj: 9.140950e+00  (min) | CPU: 931.81 MiB
│  │  ✓ | exa      | time:   8.545 s  | iters: 45    | obj: 9.140950e+00  (min) | CPU: 325.36 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
  [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
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  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
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  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
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  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
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  [33e6dc65] MKL v0.9.0
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  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
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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
  [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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  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
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  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.15
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  [10745b16] Statistics v1.11.1
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  [892a3eda] StringManipulation v0.4.1
  [856f2bd8] StructTypes v1.11.0
  [ec057cc2] StructUtils v2.6.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
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  [efce3f68] WoodburyMatrices v1.0.0
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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: `robot`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	670.342	27	9.141204	min
✓	1000	`exa_gpu`	`madnlp`	605.148	30	9.123238	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	7798.668	41	9.142359	min
✓	5000	`exa_gpu`	`madnlp`	1554.467	27	9.053093	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	19260.105	47	9.143634	min
✓	10000	`exa_gpu`	`madnlp`	3423.757	32	8.965878	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	30711.909	40	9.146361	min
✓	20000	`exa_gpu`	`madnlp`	8713.936	45	8.792951	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: robot
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 670.342 ms | iters: 27    | obj: 9.141204e+00  (min) | CPU:  42.55 MiB
│  │  ✓ | exa_gpu  | time: 605.148 ms | iters: 30    | obj: 9.123238e+00  (min) | CPU: 18.596 MiB | GPU: 66.837 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   7.799 s  | iters: 41    | obj: 9.142359e+00  (min) | CPU: 307.02 MiB
│  │  ✓ | exa_gpu  | time:   1.554 s  | iters: 27    | obj: 9.053093e+00  (min) | CPU: 29.249 MiB | GPU: 329.227 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:  19.260 s  | iters: 47    | obj: 9.143634e+00  (min) | CPU: 754.05 MiB
│  │  ✓ | exa_gpu  | time:   3.424 s  | iters: 32    | obj: 8.965878e+00  (min) | CPU: 47.575 MiB | GPU: 672.443 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:  30.712 s  | iters: 40    | obj: 9.146361e+00  (min) | CPU:   1.22 GiB
│  │  ✓ | exa_gpu  | time:   8.714 s  | iters: 45    | obj: 8.792951e+00  (min) | CPU: 86.743 MiB | GPU:  1.383 GiB
│  └─
└─