Core benchmark: rocket

This page presents benchmark results for the rocket 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
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  [ffbed154] DocStringExtensions v0.9.5
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  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
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  [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: `rocket`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	65.334	18	1.012836	max
✓	200	`adnlp`	`madnlp`	64.080	21	1.012835	max
✓	200	`exa`	`ipopt`	27.694	18	1.012836	max
✓	200	`exa`	`madnlp`	23.297	21	1.012835	max	✓
✓	200	`jump`	`ipopt`	48.787	18	1.012836	max
✓	200	`jump`	`madnlp`	53.378	21	1.012835	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	217.539	21	1.012837	max
✓	500	`adnlp`	`madnlp`	166.378	22	1.012835	max
✓	500	`exa`	`ipopt`	72.887	21	1.012837	max
✓	500	`exa`	`madnlp`	59.151	22	1.012835	max	✓
✓	500	`jump`	`ipopt`	147.958	21	1.012837	max
✓	500	`jump`	`madnlp`	140.251	22	1.012835	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	587.142	24	1.012837	max
✓	1000	`adnlp`	`madnlp`	431.178	24	1.012836	max
✓	1000	`exa`	`ipopt`	167.252	24	1.012837	max
✓	1000	`exa`	`madnlp`	132.762	24	1.012836	max	✓
✓	1000	`jump`	`ipopt`	430.870	24	1.012837	max
✓	1000	`jump`	`madnlp`	352.018	24	1.012836	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	933.176	23	1.012837	max
✓	2000	`adnlp`	`madnlp`	932.276	21	1.012830	max
✓	2000	`exa`	`ipopt`	363.288	23	1.012837	max
✓	2000	`exa`	`madnlp`	281.311	21	1.012830	max	✓
✓	2000	`jump`	`ipopt`	996.051	23	1.012837	max
✓	2000	`jump`	`madnlp`	833.681	21	1.012830	max

ℹ️ Log

Benchmarks results:

┌─ Problem: rocket
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  48.787 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU:  36.12 KiB
│  │  ✓ | adnlp    | time:  65.334 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU:  16.91 MiB
│  │  ✓ | exa      | time:  27.694 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU: 100.95 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 147.958 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU:  41.70 KiB
│  │  ✓ | adnlp    | time: 217.539 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU:  48.36 MiB
│  │  ✓ | exa      | time:  72.887 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU: 190.67 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 430.870 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU:  47.28 KiB
│  │  ✓ | adnlp    | time: 587.142 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU: 109.20 MiB
│  │  ✓ | exa      | time: 167.252 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU: 338.39 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 996.051 ms | iters: 23    | obj: 1.012837e+00  (max) | CPU:  45.42 KiB
│  │  ✓ | adnlp    | time: 933.176 ms | iters: 23    | obj: 1.012837e+00  (max) | CPU: 209.72 MiB
│  │  ✓ | exa      | time: 363.288 ms | iters: 23    | obj: 1.012837e+00  (max) | CPU: 626.42 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  53.378 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:  19.98 MiB
│  │  ✓ | adnlp    | time:  64.080 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:  23.15 MiB
│  │  ✓ | exa      | time:  23.297 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:   4.72 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 140.251 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  49.96 MiB
│  │  ✓ | adnlp    | time: 166.378 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  59.15 MiB
│  │  ✓ | exa      | time:  59.151 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  11.18 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 352.018 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU:  99.21 MiB
│  │  ✓ | adnlp    | time: 431.178 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU: 126.97 MiB
│  │  ✓ | exa      | time: 132.762 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU:  22.71 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 833.681 ms | iters: 21    | obj: 1.012830e+00  (max) | CPU: 195.09 MiB
│  │  ✓ | adnlp    | time: 932.276 ms | iters: 21    | obj: 1.012830e+00  (max) | CPU: 225.06 MiB
│  │  ✓ | exa      | time: 281.311 ms | iters: 21    | obj: 1.012830e+00  (max) | CPU:  42.07 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
  [276daf66] SpecialFunctions v2.6.1
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  [892a3eda] StringManipulation v0.4.1
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  [a759f4b9] TimerOutputs v0.5.29
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  [3bb67fe8] TranscodingStreams v0.11.3
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  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.100+0
  [e98f9f5b] NVTX_jll v3.2.2+0
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⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.8.2+2
  [629bc702] Qt6Declarative_jll v6.8.2+1
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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
  [f43a241f] Downloads v1.6.0
  [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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  [44cfe95a] Pkg v1.11.0
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  [2f01184e] SparseArrays v1.11.0
  [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
  [e37daf67] LibGit2_jll v1.7.2+0
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  [c8ffd9c3] MbedTLS_jll v2.28.6+0
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  [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
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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: `rocket`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	82.967	18	1.012836	max
✓	200	`adnlp`	`madnlp`	81.890	21	1.012835	max
✓	200	`exa`	`ipopt`	32.418	18	1.012836	max
✓	200	`exa`	`madnlp`	26.603	21	1.012835	max	✓
✓	200	`jump`	`ipopt`	56.627	18	1.012836	max
✓	200	`jump`	`madnlp`	66.121	21	1.012835	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	222.935	21	1.012837	max
✓	500	`adnlp`	`madnlp`	213.679	22	1.012835	max
✓	500	`exa`	`ipopt`	83.019	21	1.012837	max
✓	500	`exa`	`madnlp`	66.024	22	1.012835	max	✓
✓	500	`jump`	`ipopt`	162.945	21	1.012837	max
✓	500	`jump`	`madnlp`	189.119	22	1.012835	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	571.222	24	1.012837	max
✓	1000	`adnlp`	`madnlp`	535.103	24	1.012836	max
✓	1000	`exa`	`ipopt`	184.010	24	1.012837	max
✓	1000	`exa`	`madnlp`	146.967	24	1.012836	max	✓
✓	1000	`jump`	`ipopt`	429.059	24	1.012837	max
✓	1000	`jump`	`madnlp`	505.775	24	1.012836	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	1487.881	23	1.012837	max
✓	2000	`adnlp`	`madnlp`	2331.610	21	1.012830	max
✓	2000	`exa`	`ipopt`	394.673	23	1.012837	max
✓	2000	`exa`	`madnlp`	313.484	21	1.012830	max	✓
✓	2000	`jump`	`ipopt`	1075.350	23	1.012837	max
✓	2000	`jump`	`madnlp`	1066.804	21	1.012830	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	6011.617	23	1.012837	max
✓	5000	`adnlp`	`madnlp`	6172.030	24	1.012831	max
✓	5000	`exa`	`ipopt`	1185.060	23	1.012837	max
✓	5000	`exa`	`madnlp`	1083.788	24	1.012831	max	✓
✓	5000	`jump`	`ipopt`	3120.376	23	1.012837	max
✓	5000	`jump`	`madnlp`	3639.765	24	1.012831	max

ℹ️ Log

Benchmarks results:

┌─ Problem: rocket
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  56.627 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU:  36.12 KiB
│  │  ✓ | adnlp    | time:  82.967 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU:  16.91 MiB
│  │  ✓ | exa      | time:  32.418 ms | iters: 18    | obj: 1.012836e+00  (max) | CPU: 100.95 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 162.945 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU:  41.70 KiB
│  │  ✓ | adnlp    | time: 222.935 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU:  48.36 MiB
│  │  ✓ | exa      | time:  83.019 ms | iters: 21    | obj: 1.012837e+00  (max) | CPU: 190.67 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 429.059 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU:  47.28 KiB
│  │  ✓ | adnlp    | time: 571.222 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU: 109.20 MiB
│  │  ✓ | exa      | time: 184.010 ms | iters: 24    | obj: 1.012837e+00  (max) | CPU: 338.39 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   1.075 s  | iters: 23    | obj: 1.012837e+00  (max) | CPU:  45.42 KiB
│  │  ✓ | adnlp    | time:   1.488 s  | iters: 23    | obj: 1.012837e+00  (max) | CPU: 209.72 MiB
│  │  ✓ | exa      | time: 394.673 ms | iters: 23    | obj: 1.012837e+00  (max) | CPU: 626.42 KiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   3.120 s  | iters: 23    | obj: 1.012837e+00  (max) | CPU:  45.42 KiB
│  │  ✓ | adnlp    | time:   6.012 s  | iters: 23    | obj: 1.012837e+00  (max) | CPU: 523.95 MiB
│  │  ✓ | exa      | time:   1.185 s  | iters: 23    | obj: 1.012837e+00  (max) | CPU:   1.46 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  66.121 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:  19.98 MiB
│  │  ✓ | adnlp    | time:  81.890 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:  23.15 MiB
│  │  ✓ | exa      | time:  26.603 ms | iters: 21    | obj: 1.012835e+00  (max) | CPU:   4.72 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 189.119 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  49.96 MiB
│  │  ✓ | adnlp    | time: 213.679 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  59.15 MiB
│  │  ✓ | exa      | time:  66.024 ms | iters: 22    | obj: 1.012835e+00  (max) | CPU:  11.18 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 505.775 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU:  99.21 MiB
│  │  ✓ | adnlp    | time: 535.103 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU: 126.97 MiB
│  │  ✓ | exa      | time: 146.967 ms | iters: 24    | obj: 1.012836e+00  (max) | CPU:  22.71 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   1.067 s  | iters: 21    | obj: 1.012830e+00  (max) | CPU: 195.09 MiB
│  │  ✓ | adnlp    | time:   2.332 s  | iters: 21    | obj: 1.012830e+00  (max) | CPU: 225.06 MiB
│  │  ✓ | exa      | time: 313.484 ms | iters: 21    | obj: 1.012830e+00  (max) | CPU:  42.07 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   3.640 s  | iters: 24    | obj: 1.012831e+00  (max) | CPU: 491.51 MiB
│  │  ✓ | adnlp    | time:   6.172 s  | iters: 24    | obj: 1.012831e+00  (max) | CPU: 631.77 MiB
│  │  ✓ | exa      | time:   1.084 s  | iters: 24    | obj: 1.012831e+00  (max) | CPU: 111.20 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
  [1a297f60] FillArrays v1.15.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
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  [069b7b12] FunctionWrappers v1.1.3
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  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
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  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
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  [33e6dc65] MKL v0.9.0
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  [1914dd2f] MacroTools v0.5.16
  [2621e9c9] MadNLP v0.8.12
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.46.0
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
  [f4238b75] NLPModelsIpopt v0.11.0
  [e01155f1] NLPModelsModifiers v0.7.2
  [5da4648a] NVTX v1.0.1
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.1
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.0
  [43287f4e] PtrArrays v1.3.0
  [be4d8f0f] Quadmath v0.5.13
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
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  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [37e2e3b7] ReverseDiff v1.16.1
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
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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
  [62fd8b95] TensorCore v0.1.1
  [a759f4b9] TimerOutputs v0.5.29
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  [41fe7b60] Unzip v0.2.0
  [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: `rocket`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	114.080	18	1.012710	max	✓
✓	1000	`exa_gpu`	`madnlp`	597.681	47	1.000000	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	722.219	18	1.012223	max	✓
✓	5000	`exa_gpu`	`madnlp`	788.905	27	1.000007	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	1530.963	17	1.011682	max
✓	10000	`exa_gpu`	`madnlp`	1221.304	24	1.000001	max	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	3067.178	17	1.010835	max
✓	20000	`exa_gpu`	`madnlp`	2266.661	26	1.000000	max	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: rocket
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 114.080 ms | iters: 18    | obj: 1.012710e+00  (max) | CPU:  19.97 MiB
│  │  ✓ | exa_gpu  | time: 597.681 ms | iters: 47    | obj: 1.000000e+00  (max) | CPU: 20.368 MiB | GPU: 43.579 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 722.219 ms | iters: 18    | obj: 1.012223e+00  (max) | CPU:  97.64 MiB
│  │  ✓ | exa_gpu  | time: 788.905 ms | iters: 27    | obj: 1.000007e+00  (max) | CPU: 21.799 MiB | GPU: 201.423 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   1.531 s  | iters: 17    | obj: 1.011682e+00  (max) | CPU: 190.76 MiB
│  │  ✓ | exa_gpu  | time:   1.221 s  | iters: 24    | obj: 1.000001e+00  (max) | CPU: 31.664 MiB | GPU: 397.830 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   3.067 s  | iters: 17    | obj: 1.010835e+00  (max) | CPU: 380.97 MiB
│  │  ✓ | exa_gpu  | time:   2.267 s  | iters: 26    | obj: 9.999998e-01  (max) | CPU: 54.037 MiB | GPU: 801.869 MiB
│  └─
└─