Core benchmark: robbins

This page presents benchmark results for the robbins problem across different platforms and configurations.

Note

The linear solver is MUMPS for CPU experiments and CUDSS for GPU experiments.

Ubuntu Latest CPU

This benchmark suite evaluates optimal control problems on a standard CPU platform using GitHub Actions runners.

⚙️ Configuration

Problems: balanced_field, beam, brachistochrone, bryson_denham, chain, dielectrophoretic_particle, double_oscillator, ducted_fan, electric_vehicle, glider, insurance, jackson, mountain_car, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: ipopt, madnlp
Models: adnlp, exa, jump
Grid sizes: 200, 500, 1000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 500.0s wall time

🖥️ Environment

📅 Timestamp     : 2026-03-11 14:47:54 UTC
🔧 Julia version : 1.12.5
💻 OS            : Linux
🖥️ Machine       : runnervm0kj6c

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 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 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-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager

📦 Package status

Project CTBenchmarks v0.4.1
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌅ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.10.1
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.14.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.2
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [91a5bcdd] Plots v1.41.6
  [10745b16] Statistics v1.11.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

📚 Complete manifest

Project CTBenchmarks v0.4.1
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
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⌅ [54762871] CTBase v0.16.2
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⌃ [1c39547c] CTFlows v0.8.9
⌅ [34c4fa32] CTModels v0.6.9
⌅ [32681960] CTParser v0.7.2
  [052768ef] CUDA v5.10.1
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  [45b445bb] CUDSS v0.6.7
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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)

🧭 Solution: N = 200 (Ubuntu Latest CPU)

🧭 Solution: N = 500 (Ubuntu Latest CPU)

🧭 Solution: N = 1000 (Ubuntu Latest CPU)

📊 Table of Results (Ubuntu Latest CPU)

Problem: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	34.211	19	19.626260	min
✓	200	`adnlp`	`madnlp`	43.183	34	19.626260	min
✓	200	`exa`	`ipopt`	23.217	19	19.626260	min	✓
✓	200	`exa`	`madnlp`	26.402	34	19.626260	min
✓	200	`jump`	`ipopt`	25.389	19	19.626260	min
✓	200	`jump`	`madnlp`	25.708	34	19.626260	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	72.763	18	19.466633	min
✓	500	`adnlp`	`madnlp`	87.679	29	19.466633	min
✓	500	`exa`	`ipopt`	50.436	18	19.466633	min
✓	500	`exa`	`madnlp`	52.935	29	19.466633	min
✓	500	`jump`	`ipopt`	49.400	18	19.466633	min	✓
✓	500	`jump`	`madnlp`	55.233	31	19.466633	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	216.678	27	19.440191	min
✓	1000	`adnlp`	`madnlp`	322.803	50	19.440191	min
✓	1000	`exa`	`ipopt`	138.749	27	19.440191	min
✓	1000	`exa`	`madnlp`	169.978	50	19.440191	min
✓	1000	`jump`	`ipopt`	135.792	27	19.440191	min	✓
✓	1000	`jump`	`madnlp`	165.368	50	19.440191	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  25.389 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  12.16 KiB
│  │  ✓ | adnlp    | time:  34.211 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:   3.48 MiB
│  │  ✓ | exa      | time:  23.217 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  95.61 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  49.400 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:  11.16 KiB
│  │  ✓ | adnlp    | time:  72.763 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:   8.08 MiB
│  │  ✓ | exa      | time:  50.436 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU: 180.98 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 135.792 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  15.66 KiB
│  │  ✓ | adnlp    | time: 216.678 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  23.33 MiB
│  │  ✓ | exa      | time: 138.749 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU: 334.70 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  25.708 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.81 MiB
│  │  ✓ | adnlp    | time:  43.183 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   8.26 MiB
│  │  ✓ | exa      | time:  26.402 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.65 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  55.233 ms | iters: 31    | obj: 1.946663e+01  (min) | CPU:   6.14 MiB
│  │  ✓ | adnlp    | time:  87.679 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:  17.55 MiB
│  │  ✓ | exa      | time:  52.935 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   5.67 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 165.368 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  16.03 MiB
│  │  ✓ | adnlp    | time: 322.803 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  56.11 MiB
│  │  ✓ | exa      | time: 169.978 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  15.45 MiB
│  └─
└─

KKT CPU

Results on self-hosted KKT hardware.

⚙️ Configuration

Problems: balanced_field, beam, brachistochrone, bryson_denham, chain, dielectrophoretic_particle, double_oscillator, ducted_fan, electric_vehicle, glider, insurance, jackson, mountain_car, 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     : 2026-03-11 01:25:20 UTC
🔧 Julia version : 1.12.4
💻 OS            : Linux
🖥️ Machine       : kkt.mcs.anl.gov

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 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 192 × INTEL(R) XEON(R) PLATINUM 8568Y+
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, sapphirerapids)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 192 virtual cores)
Environment:
  JULIA_CUDSS_LIBRARY_PATH = /software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib
  JULIA_LOAD_PATH = @:@v#.#:@stdlib:/software/julia/environments/v1.12
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /storage/mschanen/github-actions/julia_depot
  LD_LIBRARY_PATH = /software/julia/julia_binaries/julia-1.12/lib:/software/mpich-ofi/lib:/software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib:/usr/local/cuda/lib

📦 Package status

Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌅ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.10.1
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.14.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.2
⌅ [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [91a5bcdd] Plots v1.41.6
  [10745b16] Statistics v1.11.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

📚 Complete manifest

Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.21.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.5.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.1
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌅ [54762871] CTBase v0.16.2
⌅ [790bbbee] CTDirect v0.17.5-beta
⌃ [1c39547c] CTFlows v0.8.12-beta
⌅ [34c4fa32] CTModels v0.6.10-beta.2
⌅ [32681960] CTParser v0.7.3-beta
  [052768ef] CUDA v5.10.1
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.7
  [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 v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.1
  [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 v0.9.3
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.16.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.2
  [069b7b12] FunctionWrappers v1.1.3
  [0c68f7d7] GPUArrays v11.4.1
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.8.2
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.24
  [42e2da0e] Grisu v1.0.2
  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.11.0
  [076d061b] HashArrayMappedTries v0.2.0
  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.14.1
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
  [63c18a36] KernelAbstractions v0.9.40
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.6
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [5c8ed15e] LinearOperators v2.13.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [33e6dc65] MKL v0.9.1
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
⌅ [2621e9c9] MadNLP v0.8.12
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.49.0
  [739be429] MbedTLS v1.1.10
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.11
  [f4238b75] NLPModelsIpopt v0.11.2
  [e01155f1] NLPModelsModifiers v0.7.4
  [5da4648a] NVTX v1.0.3
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.1
⌅ [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [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 v1.41.6
  [2dfb63ee] PooledArrays v1.4.3
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.2
  [08abe8d2] PrettyTables v3.2.3
  [43287f4e] PtrArrays v1.4.0
  [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 v1.16.2
  [7e506255] ScopedValues v1.6.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.9
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.10
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.2.1
  [0a514795] SparseMatrixColorings v0.4.24
  [276daf66] SpecialFunctions v2.7.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.17
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.10
  [892a3eda] StringManipulation v0.4.4
  [ec057cc2] StructUtils v2.6.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [a759f4b9] TimerOutputs v0.5.29
  [e689c965] Tracy v0.1.6
  [3bb67fe8] TranscodingStreams v0.11.3
  [5c2747f8] URIs v1.6.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [efce3f68] WoodburyMatrices v1.1.0
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [d1e2174e] CUDA_Compiler_jll v0.4.1+1
  [4ee394cb] CUDA_Driver_jll v13.1.1+0
  [76a88914] CUDA_Runtime_jll v0.20.1+0
  [4889d778] CUDSS_jll v0.7.1+0
  [83423d85] Cairo_jll v1.18.5+1
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.7.3+0
  [b22a6f82] FFMPEG_jll v8.0.1+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.4.1+0
  [d2c73de3] GR_jll v0.73.24+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.86.3+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [017b0a0e] HSL_jll v4.0.4+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [e33a78d0] Hwloc_jll v2.13.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1901+0
  [aacddb02] JpegTurbo_jll v3.1.4+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [dad2f222] LLVMExtra_jll v0.0.38+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [ad6e5548] LibTracyClient_jll v0.13.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.3+0
  [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.41.3+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.200+0
  [c8ffd9c3] MbedTLS_jll v2.28.1010+0
  [e98f9f5b] NVTX_jll v3.2.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.30+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.10.2+1
  [629bc702] Qt6Declarative_jll v6.10.2+1
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [319450e9] SPRAL_jll v2025.9.18+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
⌅ [02c8fc9c] XML2_jll v2.13.9+0
  [ffd25f8a] XZ_jll v5.8.2+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.3+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.18.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [1e29f10c] demumble_jll v1.3.0+0
  [35ca27e7] eudev_jll v3.2.14+0
  [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.13.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.55+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
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  [4607b0f0] SuiteSparse
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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 (KKT CPU)

🧭 Solution: N = 200 (KKT CPU)

🧭 Solution: N = 500 (KKT CPU)

🧭 Solution: N = 1000 (KKT CPU)

🧭 Solution: N = 2000 (KKT CPU)

📊 Table of Results (KKT CPU)

Problem: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	24.047	19	19.626260	min
✓	200	`adnlp`	`madnlp`	31.795	34	19.626260	min
✓	200	`exa`	`ipopt`	14.088	19	19.626260	min	✓
✓	200	`exa`	`madnlp`	15.838	34	19.626260	min
✓	200	`jump`	`ipopt`	14.891	19	19.626260	min
✓	200	`jump`	`madnlp`	15.586	34	19.626260	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	55.188	18	19.466633	min
✓	500	`adnlp`	`madnlp`	68.920	31	19.466633	min
✓	500	`exa`	`ipopt`	31.745	18	19.466633	min	✓
✓	500	`exa`	`madnlp`	33.499	29	19.466633	min
✓	500	`jump`	`ipopt`	32.547	18	19.466633	min
✓	500	`jump`	`madnlp`	33.164	29	19.466633	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	147.388	27	19.440191	min
✓	1000	`adnlp`	`madnlp`	217.732	50	19.440191	min
✓	1000	`exa`	`ipopt`	88.906	27	19.440191	min	✓
✓	1000	`exa`	`madnlp`	109.552	50	19.440191	min
✓	1000	`jump`	`ipopt`	89.172	27	19.440191	min
✓	1000	`jump`	`madnlp`	108.136	50	19.440191	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	322.854	30	19.433915	min
✓	2000	`adnlp`	`madnlp`	444.274	44	19.433916	min
✓	2000	`exa`	`ipopt`	206.006	30	19.433915	min
✓	2000	`exa`	`madnlp`	265.859	43	19.433916	min
✓	2000	`jump`	`ipopt`	198.687	30	19.433915	min	✓
✓	2000	`jump`	`madnlp`	239.620	43	19.433916	min

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  14.891 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  12.16 KiB
│  │  ✓ | adnlp    | time:  24.047 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:   3.50 MiB
│  │  ✓ | exa      | time:  14.088 ms | iters: 19    | obj: 1.962626e+01  (min) | CPU:  95.61 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  32.547 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:  11.16 KiB
│  │  ✓ | adnlp    | time:  55.188 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU:   8.08 MiB
│  │  ✓ | exa      | time:  31.745 ms | iters: 18    | obj: 1.946663e+01  (min) | CPU: 180.98 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  89.172 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  15.66 KiB
│  │  ✓ | adnlp    | time: 147.388 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU:  23.33 MiB
│  │  ✓ | exa      | time:  88.906 ms | iters: 27    | obj: 1.944019e+01  (min) | CPU: 334.70 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 198.687 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  17.16 KiB
│  │  ✓ | adnlp    | time: 322.854 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU:  51.38 MiB
│  │  ✓ | exa      | time: 206.006 ms | iters: 30    | obj: 1.943391e+01  (min) | CPU: 626.86 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  15.586 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.81 MiB
│  │  ✓ | adnlp    | time:  31.795 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   8.26 MiB
│  │  ✓ | exa      | time:  15.838 ms | iters: 34    | obj: 1.962626e+01  (min) | CPU:   2.65 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  33.164 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   5.87 MiB
│  │  ✓ | adnlp    | time:  68.920 ms | iters: 31    | obj: 1.946663e+01  (min) | CPU:  18.72 MiB
│  │  ✓ | exa      | time:  33.499 ms | iters: 29    | obj: 1.946663e+01  (min) | CPU:   5.67 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 108.136 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  16.03 MiB
│  │  ✓ | adnlp    | time: 217.732 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  56.11 MiB
│  │  ✓ | exa      | time: 109.552 ms | iters: 50    | obj: 1.944019e+01  (min) | CPU:  15.45 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 239.620 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  28.89 MiB
│  │  ✓ | adnlp    | time: 444.274 ms | iters: 44    | obj: 1.943392e+01  (min) | CPU:  99.55 MiB
│  │  ✓ | exa      | time: 265.859 ms | iters: 43    | obj: 1.943392e+01  (min) | CPU:  27.55 MiB
│  └─
└─

KKT GPU

Results on self-hosted KKT hardware.

⚙️ Configuration

Problems: balanced_field, beam, brachistochrone, bryson_denham, chain, dielectrophoretic_particle, double_oscillator, ducted_fan, electric_vehicle, glider, insurance, jackson, mountain_car, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: madnlp
Models: exa, exa_gpu
Grid sizes: 1000, 5000, 10000, 20000 discretization points
Discretization: midpoint method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 2000.0s wall time

🖥️ Environment

📅 Timestamp     : 2026-03-10 19:50:42 UTC
🔧 Julia version : 1.12.4
💻 OS            : Linux
🖥️ Machine       : kkt.mcs.anl.gov

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 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 192 × INTEL(R) XEON(R) PLATINUM 8568Y+
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, sapphirerapids)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 192 virtual cores)
Environment:
  JULIA_CUDSS_LIBRARY_PATH = /software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib
  JULIA_LOAD_PATH = @:@v#.#:@stdlib:/software/julia/environments/v1.12
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /storage/mschanen/github-actions/julia_depot
  LD_LIBRARY_PATH = /software/julia/julia_binaries/julia-1.12/lib:/software/mpich-ofi/lib:/software/libcudss/libcudss-linux-x86_64-0.7.1.4_cuda13-archive/lib:/usr/local/cuda/lib

📦 Package status

Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌅ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.10.1
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.14.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.2
⌅ [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [91a5bcdd] Plots v1.41.6
  [10745b16] Statistics v1.11.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

📚 Complete manifest

Project CTBenchmarks v0.3.1
Status `/storage/mschanen/github-actions/actions_runner_ct/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.21.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.5.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.1
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌅ [54762871] CTBase v0.16.2
⌅ [790bbbee] CTDirect v0.17.5-beta
⌃ [1c39547c] CTFlows v0.8.12-beta
⌅ [34c4fa32] CTModels v0.6.10-beta.2
⌅ [32681960] CTParser v0.7.3-beta
  [052768ef] CUDA v5.10.1
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.7
  [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 v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.1
  [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 v0.9.3
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.16.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.2
  [069b7b12] FunctionWrappers v1.1.3
  [0c68f7d7] GPUArrays v11.4.1
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.8.2
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.24
  [42e2da0e] Grisu v1.0.2
  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.11.0
  [076d061b] HashArrayMappedTries v0.2.0
  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.14.1
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.30.0
  [63c18a36] KernelAbstractions v0.9.40
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.6
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [5c8ed15e] LinearOperators v2.13.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [33e6dc65] MKL v0.9.1
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
⌅ [2621e9c9] MadNLP v0.8.12
⌅ [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.49.0
  [739be429] MbedTLS v1.1.10
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.11
  [f4238b75] NLPModelsIpopt v0.11.2
  [e01155f1] NLPModelsModifiers v0.7.4
  [5da4648a] NVTX v1.0.3
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.1
⌅ [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.5.0
  [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 v1.41.6
  [2dfb63ee] PooledArrays v1.4.3
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.2
  [08abe8d2] PrettyTables v3.2.3
  [43287f4e] PtrArrays v1.4.0
  [be4d8f0f] Quadmath v0.5.13
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  [37e2e3b7] ReverseDiff v1.16.2
  [7e506255] ScopedValues v1.6.0
  [6c6a2e73] Scratch v1.3.0
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  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
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  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.10
  [892a3eda] StringManipulation v0.4.4
  [ec057cc2] StructUtils v2.6.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [a759f4b9] TimerOutputs v0.5.29
  [e689c965] Tracy v0.1.6
  [3bb67fe8] TranscodingStreams v0.11.3
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  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [efce3f68] WoodburyMatrices v1.1.0
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [d1e2174e] CUDA_Compiler_jll v0.4.1+1
  [4ee394cb] CUDA_Driver_jll v13.1.1+0
  [76a88914] CUDA_Runtime_jll v0.20.1+0
  [4889d778] CUDSS_jll v0.7.1+0
  [83423d85] Cairo_jll v1.18.5+1
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.7.3+0
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  [3b182d85] Graphite2_jll v1.3.15+0
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  [e33a78d0] Hwloc_jll v2.13.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1901+0
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  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

📈 Time vs Grid Size (KKT GPU)

🧭 Solution: N = 1000 (KKT GPU)

🧭 Solution: N = 5000 (KKT GPU)

🧭 Solution: N = 10000 (KKT GPU)

🧭 Solution: N = 20000 (KKT GPU)

📊 Table of Results (KKT GPU)

Problem: `robbins`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	180.261	44	19.433173	min	✓
✓	1000	`exa_gpu`	`madnlp`	269.726	44	19.432981	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	1213.703	75	19.431842	min
✓	5000	`exa_gpu`	`madnlp`	269.358	49	19.430932	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	2113.663	63	19.431807	min
✓	10000	`exa_gpu`	`madnlp`	556.052	96	19.429991	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	5656.143	71	19.431808	min
✓	20000	`exa_gpu`	`madnlp`	941.567	132	19.428183	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: robbins
│
├──┬ Solver: madnlp, Discretization: midpoint
│  │
│  │  N = 1000
│  │  ✓ | exa      | time: 180.261 ms | iters: 44    | obj: 1.943317e+01  (min) | CPU:  14.02 MiB
│  │  ✓ | exa_gpu  | time: 269.726 ms | iters: 44    | obj: 1.943298e+01  (min) | CPU: 13.448 MiB | GPU: 18.338 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time:   1.214 s  | iters: 75    | obj: 1.943184e+01  (min) | CPU: 100.45 MiB
│  │  ✓ | exa_gpu  | time: 269.358 ms | iters: 49    | obj: 1.943093e+01  (min) | CPU: 17.776 MiB | GPU: 94.103 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time:   2.114 s  | iters: 63    | obj: 1.943181e+01  (min) | CPU: 176.24 MiB
│  │  ✓ | exa_gpu  | time: 556.052 ms | iters: 96    | obj: 1.942999e+01  (min) | CPU: 34.292 MiB | GPU: 237.016 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time:   5.656 s  | iters: 71    | obj: 1.943181e+01  (min) | CPU: 386.61 MiB
│  │  ✓ | exa_gpu  | time: 941.567 ms | iters: 132   | obj: 1.942818e+01  (min) | CPU: 51.031 MiB | GPU: 547.984 MiB
│  └─
└─