Core benchmark: insurance

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

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	535.868	90	2.058581	max
✓	200	`adnlp`	`madnlp`	674.460	120	2.058581	max
✓	200	`exa`	`ipopt`	321.088	91	2.058581	max	✓
✓	200	`exa`	`madnlp`	338.467	120	2.058581	max
✓	200	`jump`	`ipopt`	404.531	91	2.058581	max
✓	200	`jump`	`madnlp`	451.160	120	2.058581	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	1544.801	96	2.059214	max
✓	500	`adnlp`	`madnlp`	6799.569	409	2.059207	max
✓	500	`exa`	`ipopt`	894.937	109	2.059214	max	✓
✓	500	`exa`	`madnlp`	3202.164	350	2.059213	max
✓	500	`jump`	`ipopt`	1060.430	105	2.059214	max
✓	500	`jump`	`madnlp`	2775.363	255	2.059207	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	4880.833	146	2.059511	max
✓	1000	`adnlp`	`madnlp`	17577.720	529	2.059510	max
✓	1000	`exa`	`ipopt`	2581.408	134	2.059511	max	✓
✓	1000	`exa`	`madnlp`	9231.085	520	2.059510	max
✓	1000	`jump`	`ipopt`	3148.649	144	2.059511	max
✓	1000	`jump`	`madnlp`	12189.582	567	2.059511	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	16693.827	194	2.059700	max
✓	2000	`adnlp`	`madnlp`	16623.738	171	2.059697	max
✓	2000	`exa`	`ipopt`	6746.631	194	2.059700	max	✓
✓	2000	`exa`	`madnlp`	6793.265	171	2.059697	max
✓	2000	`jump`	`ipopt`	11467.873	219	2.059700	max
✓	2000	`jump`	`madnlp`	10044.427	171	2.059697	max

ℹ️ Log

Benchmarks results:

┌─ Problem: insurance
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 404.531 ms | iters: 91    | obj: 2.058581e+00  (max) | CPU: 179.67 KiB
│  │  ✓ | adnlp    | time: 535.868 ms | iters: 90    | obj: 2.058581e+00  (max) | CPU: 120.76 MiB
│  │  ✓ | exa      | time: 321.088 ms | iters: 91    | obj: 2.058581e+00  (max) | CPU: 246.03 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   1.060 s  | iters: 105   | obj: 2.059214e+00  (max) | CPU: 198.28 KiB
│  │  ✓ | adnlp    | time:   1.545 s  | iters: 96    | obj: 2.059214e+00  (max) | CPU: 312.00 MiB
│  │  ✓ | exa      | time: 894.937 ms | iters: 109   | obj: 2.059214e+00  (max) | CPU: 441.50 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   3.149 s  | iters: 144   | obj: 2.059511e+00  (max) | CPU: 273.53 KiB
│  │  ✓ | adnlp    | time:   4.881 s  | iters: 146   | obj: 2.059511e+00  (max) | CPU: 946.02 MiB
│  │  ✓ | exa      | time:   2.581 s  | iters: 134   | obj: 2.059511e+00  (max) | CPU: 769.39 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  11.468 s  | iters: 219   | obj: 2.059700e+00  (max) | CPU: 418.45 KiB
│  │  ✓ | adnlp    | time:  16.694 s  | iters: 194   | obj: 2.059700e+00  (max) | CPU:   2.46 GiB
│  │  ✓ | exa      | time:   6.747 s  | iters: 194   | obj: 2.059700e+00  (max) | CPU:   1.40 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 451.160 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU:  36.15 MiB
│  │  ✓ | adnlp    | time: 674.460 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU: 200.56 MiB
│  │  ✓ | exa      | time: 338.467 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU:  26.53 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   2.775 s  | iters: 255   | obj: 2.059207e+00  (max) | CPU: 138.17 MiB
│  │  ✓ | adnlp    | time:   6.800 s  | iters: 409   | obj: 2.059207e+00  (max) | CPU:   1.52 GiB
│  │  ✓ | exa      | time:   3.202 s  | iters: 350   | obj: 2.059213e+00  (max) | CPU: 156.60 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  12.190 s  | iters: 567   | obj: 2.059511e+00  (max) | CPU: 522.90 MiB
│  │  ✓ | adnlp    | time:  17.578 s  | iters: 529   | obj: 2.059510e+00  (max) | CPU:   3.76 GiB
│  │  ✓ | exa      | time:   9.231 s  | iters: 520   | obj: 2.059510e+00  (max) | CPU: 435.45 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  10.044 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU: 416.25 MiB
│  │  ✓ | adnlp    | time:  16.624 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU:   2.56 GiB
│  │  ✓ | exa      | time:   6.793 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU: 321.89 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
  [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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  [777ac1f9] SimpleBufferStream v1.2.0
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  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
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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
  [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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  [0dad84c5] ArgTools v1.1.2
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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
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
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  [44cfe95a] Pkg v1.11.0
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  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
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  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [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
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [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: `insurance`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	642.744	90	2.058581	max
✓	200	`adnlp`	`madnlp`	971.339	120	2.058581	max
✓	200	`exa`	`ipopt`	354.264	90	2.058581	max	✓
✓	200	`exa`	`madnlp`	383.745	120	2.058581	max
✓	200	`jump`	`ipopt`	466.118	91	2.058581	max
✓	200	`jump`	`madnlp`	562.179	120	2.058581	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	1490.137	87	2.059208	max
✓	500	`adnlp`	`madnlp`	9057.109	363	2.059213	max
✓	500	`exa`	`ipopt`	883.976	97	2.059214	max	✓
✓	500	`exa`	`madnlp`	2567.325	264	2.059213	max
✓	500	`jump`	`ipopt`	977.661	89	2.059208	max
✓	500	`jump`	`madnlp`	3441.772	254	2.059213	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	5458.479	140	2.059511	max
✓	1000	`adnlp`	`madnlp`	32535.132	635	2.059510	max
✓	1000	`exa`	`ipopt`	3204.118	149	2.059511	max	✓
✓	1000	`exa`	`madnlp`	13549.701	646	2.059510	max
✓	1000	`jump`	`ipopt`	3910.102	150	2.059511	max
✓	1000	`jump`	`madnlp`	13130.290	494	2.059510	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	22773.237	193	2.059700	max
✓	2000	`adnlp`	`madnlp`	21106.936	171	2.059697	max
✓	2000	`exa`	`ipopt`	10446.747	223	2.059700	max
✓	2000	`exa`	`madnlp`	7929.872	171	2.059697	max	✓
✓	2000	`jump`	`ipopt`	11803.489	199	2.059700	max
✓	2000	`jump`	`madnlp`	12598.288	171	2.059697	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	111443.993	350	2.059854	max
✓	5000	`adnlp`	`madnlp`	215708.889	738	2.059852	max
✓	5000	`exa`	`ipopt`	52828.034	360	2.059854	max	✓
✓	5000	`exa`	`madnlp`	86659.768	767	2.059845	max
✓	5000	`jump`	`ipopt`	74269.862	388	2.059859	max
✓	5000	`jump`	`madnlp`	135338.407	810	2.059855	max

ℹ️ Log

Benchmarks results:

┌─ Problem: insurance
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 466.118 ms | iters: 91    | obj: 2.058581e+00  (max) | CPU: 179.28 KiB
│  │  ✓ | adnlp    | time: 642.744 ms | iters: 90    | obj: 2.058581e+00  (max) | CPU: 121.36 MiB
│  │  ✓ | exa      | time: 354.264 ms | iters: 90    | obj: 2.058581e+00  (max) | CPU: 246.02 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 977.661 ms | iters: 89    | obj: 2.059208e+00  (max) | CPU: 168.92 KiB
│  │  ✓ | adnlp    | time:   1.490 s  | iters: 87    | obj: 2.059208e+00  (max) | CPU: 283.32 MiB
│  │  ✓ | exa      | time: 883.976 ms | iters: 97    | obj: 2.059214e+00  (max) | CPU: 429.12 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:   3.910 s  | iters: 150   | obj: 2.059511e+00  (max) | CPU: 289.38 KiB
│  │  ✓ | adnlp    | time:   5.458 s  | iters: 140   | obj: 2.059511e+00  (max) | CPU: 909.61 MiB
│  │  ✓ | exa      | time:   3.204 s  | iters: 149   | obj: 2.059511e+00  (max) | CPU: 785.88 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  11.803 s  | iters: 199   | obj: 2.059700e+00  (max) | CPU: 378.14 KiB
│  │  ✓ | adnlp    | time:  22.773 s  | iters: 193   | obj: 2.059700e+00  (max) | CPU:   2.44 GiB
│  │  ✓ | exa      | time:  10.447 s  | iters: 223   | obj: 2.059700e+00  (max) | CPU:   1.43 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time:  74.270 s  | iters: 388   | obj: 2.059859e+00  (max) | CPU: 761.20 KiB
│  │  ✓ | adnlp    | time: 111.444 s  | iters: 350   | obj: 2.059854e+00  (max) | CPU:  11.16 GiB
│  │  ✓ | exa      | time:  52.828 s  | iters: 360   | obj: 2.059854e+00  (max) | CPU:   3.35 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time: 562.179 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU:  36.15 MiB
│  │  ✓ | adnlp    | time: 971.339 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU: 200.56 MiB
│  │  ✓ | exa      | time: 383.745 ms | iters: 120   | obj: 2.058581e+00  (max) | CPU:  26.53 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   3.442 s  | iters: 254   | obj: 2.059213e+00  (max) | CPU: 152.45 MiB
│  │  ✓ | adnlp    | time:   9.057 s  | iters: 363   | obj: 2.059213e+00  (max) | CPU:   1.31 GiB
│  │  ✓ | exa      | time:   2.567 s  | iters: 264   | obj: 2.059213e+00  (max) | CPU: 118.57 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  13.130 s  | iters: 494   | obj: 2.059510e+00  (max) | CPU: 468.95 MiB
│  │  ✓ | adnlp    | time:  32.535 s  | iters: 635   | obj: 2.059510e+00  (max) | CPU:   4.52 GiB
│  │  ✓ | exa      | time:  13.550 s  | iters: 646   | obj: 2.059510e+00  (max) | CPU: 550.25 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  12.598 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU: 416.27 MiB
│  │  ✓ | adnlp    | time:  21.107 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU:   2.56 GiB
│  │  ✓ | exa      | time:   7.930 s  | iters: 171   | obj: 2.059697e+00  (max) | CPU: 321.91 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time: 135.338 s  | iters: 810   | obj: 2.059855e+00  (max) | CPU:   3.47 GiB
│  │  ✓ | adnlp    | time: 215.709 s  | iters: 738   | obj: 2.059852e+00  (max) | CPU:  26.06 GiB
│  │  ✓ | exa      | time:  86.660 s  | iters: 767   | obj: 2.059845e+00  (max) | CPU:   3.08 GiB
│  └─
└─

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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  [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
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [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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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: `insurance`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	10683.405	538	2.059433	max
✓	1000	`exa_gpu`	`madnlp`	583.339	61	1.175172	max	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	90842.301	752	2.059534	max
✓	5000	`exa_gpu`	`madnlp`	3760.057	240	1.173337	max	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	150341.809	558	2.059237	max
✓	10000	`exa_gpu`	`madnlp`	9027.410	282	1.171076	max	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	398139.291	636	2.058537	max
✓	20000	`exa_gpu`	`madnlp`	4027.237	76	1.166456	max	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: insurance
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  10.683 s  | iters: 538   | obj: 2.059433e+00  (max) | CPU: 462.87 MiB
│  │  ✓ | exa_gpu  | time: 583.339 ms | iters: 61    | obj: 1.175172e+00  (max) | CPU: 28.462 MiB | GPU: 57.504 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:  90.842 s  | iters: 752   | obj: 2.059534e+00  (max) | CPU:   3.20 GiB
│  │  ✓ | exa_gpu  | time:   3.760 s  | iters: 240   | obj: 1.173337e+00  (max) | CPU: 111.790 MiB | GPU: 586.527 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 150.342 s  | iters: 558   | obj: 2.059237e+00  (max) | CPU:   4.81 GiB
│  │  ✓ | exa_gpu  | time:   9.027 s  | iters: 282   | obj: 1.171076e+00  (max) | CPU: 138.526 MiB | GPU:  1.296 GiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 398.139 s  | iters: 636   | obj: 2.058537e+00  (max) | CPU:  12.56 GiB
│  │  ✓ | exa_gpu  | time:   4.027 s  | iters: 76    | obj: 1.166456e+00  (max) | CPU: 71.554 MiB | GPU:  1.216 GiB
│  └─
└─