Core benchmark: robbins

This page presents benchmark results for the robbins 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
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  [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: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	33.542	19	19.626260	min
✓	200	`adnlp`	`madnlp`	44.031	34	19.626260	min
✓	200	`exa`	`ipopt`	23.500	19	19.626260	min	✓
✓	200	`exa`	`madnlp`	27.560	34	19.626260	min
✓	200	`jump`	`ipopt`	24.863	19	19.626260	min
✓	200	`jump`	`madnlp`	26.700	34	19.626260	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	70.958	18	19.466633	min
✓	500	`adnlp`	`madnlp`	86.884	29	19.466633	min
✓	500	`exa`	`ipopt`	51.924	18	19.466633	min
✓	500	`exa`	`madnlp`	53.861	29	19.466633	min
✓	500	`jump`	`ipopt`	51.743	18	19.466633	min	✓
✓	500	`jump`	`madnlp`	56.077	31	19.466633	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	210.191	27	19.440191	min
✓	1000	`adnlp`	`madnlp`	332.084	50	19.440191	min
✓	1000	`exa`	`ipopt`	139.435	27	19.440191	min
✓	1000	`exa`	`madnlp`	172.922	50	19.440191	min
✓	1000	`jump`	`ipopt`	136.648	27	19.440191	min	✓
✓	1000	`jump`	`madnlp`	171.187	50	19.440191	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	582.715	30	19.433915	min
✓	2000	`adnlp`	`madnlp`	759.364	43	19.433916	min
✓	2000	`exa`	`ipopt`	320.649	30	19.433915	min
✓	2000	`exa`	`madnlp`	384.560	43	19.433916	min
✓	2000	`jump`	`ipopt`	301.335	30	19.433915	min	✓
✓	2000	`jump`	`madnlp`	352.248	43	19.433916	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  24.863 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  20.03 KiB
│  │  ✓ | adnlp    | time:  33.542 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:   3.48 MiB
│  │  ✓ | exa      | time:  23.500 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  95.55 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  51.743 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:  18.41 KiB
│  │  ✓ | adnlp    | time:  70.958 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:   8.08 MiB
│  │  ✓ | exa      | time:  51.924 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU: 180.92 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 136.648 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  26.03 KiB
│  │  ✓ | adnlp    | time: 210.191 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  23.33 MiB
│  │  ✓ | exa      | time: 139.435 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU: 334.64 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 301.335 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  28.56 KiB
│  │  ✓ | adnlp    | time: 582.715 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  51.38 MiB
│  │  ✓ | exa      | time: 320.649 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU: 626.80 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  26.700 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   3.20 MiB
│  │  ✓ | adnlp    | time:  44.031 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   8.57 MiB
│  │  ✓ | exa      | time:  27.560 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.95 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  56.077 ms | iters: 31    | obj: 1.946663e+01  (min) | CPU:   6.63 MiB
│  │  ✓ | adnlp    | time:  86.884 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:  17.86 MiB
│  │  ✓ | exa      | time:  53.861 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   5.98 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 171.187 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  17.09 MiB
│  │  ✓ | adnlp    | time: 332.084 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  56.41 MiB
│  │  ✓ | exa      | time: 172.922 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  15.75 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 352.248 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  28.73 MiB
│  │  ✓ | adnlp    | time: 759.364 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  97.84 MiB
│  │  ✓ | exa      | time: 384.560 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  27.86 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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  [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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  [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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  [3bb67fe8] TranscodingStreams v0.11.3
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  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.100+0
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⌅ [30392449] Pixman_jll v0.44.2+0
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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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  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
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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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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: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	37.527	19	19.626260	min
✓	200	`adnlp`	`madnlp`	49.292	34	19.626260	min
✓	200	`exa`	`ipopt`	26.479	19	19.626260	min	✓
✓	200	`exa`	`madnlp`	28.954	34	19.626260	min
✓	200	`jump`	`ipopt`	26.831	19	19.626260	min
✓	200	`jump`	`madnlp`	29.363	34	19.626260	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	80.752	18	19.466633	min
✓	500	`adnlp`	`madnlp`	102.997	31	19.466633	min
✓	500	`exa`	`ipopt`	55.907	18	19.466633	min
✓	500	`exa`	`madnlp`	56.758	29	19.466633	min
✓	500	`jump`	`ipopt`	53.812	18	19.466633	min	✓
✓	500	`jump`	`madnlp`	56.395	29	19.466633	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	241.462	27	19.440191	min
✓	1000	`adnlp`	`madnlp`	365.345	50	19.440191	min
✓	1000	`exa`	`ipopt`	146.147	27	19.440191	min
✓	1000	`exa`	`madnlp`	181.830	50	19.440191	min
✓	1000	`jump`	`ipopt`	143.101	27	19.440191	min	✓
✓	1000	`jump`	`madnlp`	182.123	50	19.440191	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	701.197	30	19.433915	min
✓	2000	`adnlp`	`madnlp`	1021.729	44	19.433916	min
✓	2000	`exa`	`ipopt`	325.356	30	19.433915	min
✓	2000	`exa`	`madnlp`	446.429	43	19.433916	min
✓	2000	`jump`	`ipopt`	313.943	30	19.433915	min	✓
✓	2000	`jump`	`madnlp`	406.371	43	19.433916	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	3698.795	48	19.432123	min
✓	5000	`adnlp`	`madnlp`	4848.830	77	19.432125	min
✓	5000	`exa`	`ipopt`	1072.940	37	19.432124	min	✓
✓	5000	`exa`	`madnlp`	1947.202	77	19.432125	min
✓	5000	`jump`	`ipopt`	1268.797	36	19.432131	min
✓	5000	`jump`	`madnlp`	1898.192	77	19.432125	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  26.831 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  20.03 KiB
│  │  ✓ | adnlp    | time:  37.527 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:   3.50 MiB
│  │  ✓ | exa      | time:  26.479 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  95.55 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  53.812 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:  18.41 KiB
│  │  ✓ | adnlp    | time:  80.752 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:   8.08 MiB
│  │  ✓ | exa      | time:  55.907 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU: 180.92 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 143.101 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  26.03 KiB
│  │  ✓ | adnlp    | time: 241.462 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  23.33 MiB
│  │  ✓ | exa      | time: 146.147 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU: 334.64 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 313.943 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  28.56 KiB
│  │  ✓ | adnlp    | time: 701.197 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  51.38 MiB
│  │  ✓ | exa      | time: 325.356 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU: 626.80 KiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   1.269 s  | iters: 36    | obj: 1.943213e+01  (min) | CPU:  34.41 KiB
│  │  ✓ | adnlp    | time:   3.699 s  | iters: 48    | obj: 1.943212e+01  (min) | CPU: 200.45 MiB
│  │  ✓ | exa      | time:   1.073 s  | iters: 37    | obj: 1.943212e+01  (min) | CPU:   1.47 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  29.363 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   3.20 MiB
│  │  ✓ | adnlp    | time:  49.292 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   8.57 MiB
│  │  ✓ | exa      | time:  28.954 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.95 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  56.395 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   6.36 MiB
│  │  ✓ | adnlp    | time: 102.997 ms | iters: 31    | obj: 1.946663e+01  (min) | CPU:  19.03 MiB
│  │  ✓ | exa      | time:  56.758 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   5.98 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 182.123 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  17.09 MiB
│  │  ✓ | adnlp    | time: 365.345 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  56.41 MiB
│  │  ✓ | exa      | time: 181.830 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  15.75 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 406.371 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  28.73 MiB
│  │  ✓ | adnlp    | time:   1.022 s  | iters: 44    | obj: 1.943392e+01  (min) | CPU:  99.86 MiB
│  │  ✓ | exa      | time: 446.429 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  27.86 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:   1.898 s  | iters: 77    | obj: 1.943213e+01  (min) | CPU: 105.99 MiB
│  │  ✓ | adnlp    | time:   4.849 s  | iters: 77    | obj: 1.943213e+01  (min) | CPU: 415.00 MiB
│  │  ✓ | exa      | time:   1.947 s  | iters: 77    | obj: 1.943213e+01  (min) | CPU: 103.89 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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  [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
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  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
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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
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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 v0.21.5
  [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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  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
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  [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
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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: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	166.847	47	19.440235	min	✓
✓	1000	`exa_gpu`	`madnlp`	199.737	25	19.421595	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	1869.540	63	19.432348	min
✓	5000	`exa_gpu`	`madnlp`	941.778	107	19.340956	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	2971.047	43	19.432324	min
✓	10000	`exa_gpu`	`madnlp`	919.525	88	19.250629	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	8392.118	60	19.432735	min
✓	20000	`exa_gpu`	`madnlp`	2669.080	203	19.071924	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 166.847 ms | iters: 47    | obj: 1.944023e+01  (min) | CPU:  15.11 MiB
│  │  ✓ | exa_gpu  | time: 199.737 ms | iters: 25    | obj: 1.942160e+01  (min) | CPU: 10.044 MiB | GPU: 17.509 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.870 s  | iters: 63    | obj: 1.943235e+01  (min) | CPU:  89.39 MiB
│  │  ✓ | exa_gpu  | time: 941.778 ms | iters: 107   | obj: 1.934096e+01  (min) | CPU: 39.933 MiB | GPU: 130.364 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.971 s  | iters: 43    | obj: 1.943232e+01  (min) | CPU: 136.58 MiB
│  │  ✓ | exa_gpu  | time: 919.525 ms | iters: 88    | obj: 1.925063e+01  (min) | CPU: 37.539 MiB | GPU: 240.557 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   8.392 s  | iters: 60    | obj: 1.943274e+01  (min) | CPU: 342.63 MiB
│  │  ✓ | exa_gpu  | time:   2.669 s  | iters: 203   | obj: 1.907192e+01  (min) | CPU: 82.771 MiB | GPU: 719.887 MiB
│  └─
└─