Core benchmark: balanced_field

This page presents benchmark results for the balanced_field 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: balanced_field
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     : 2026-02-13 09:36:08 UTC
🔧 Julia version : 1.11.9
💻 OS            : Linux
🖥️ Machine       : runnervmjduv7

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 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 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 v0.3.1
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌅ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.6
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.14.0
  [682c06a0] JSON v1.4.0
  [4076af6c] JuMP v1.29.4
  [d72a61cc] MadNLPGPU v0.7.18
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.1
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.4.0 `https://github.com/control-toolbox/OptimalControlProblems.jl#202-general-new-problem-the-van-der-pol-oscillator`
  [91a5bcdd] Plots v1.41.5
  [10745b16] Statistics v1.11.1
  [bd369af6] Tables v1.12.1
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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 but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

📚 Complete manifest

Project CTBenchmarks v0.3.1
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them 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: `balanced_field`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	96.244	17	771.011400	min
✓	200	`adnlp`	`madnlp`	148.208	23	771.011400	min
✓	200	`exa`	`ipopt`	39.684	17	771.011400	min	✓
✓	200	`exa`	`madnlp`	39.870	23	771.011400	min
✓	200	`jump`	`ipopt`	72.376	17	771.011400	min
✓	200	`jump`	`madnlp`	99.835	23	771.011400	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	311.994	20	771.008497	min
✓	500	`adnlp`	`madnlp`	366.933	25	771.008498	min
✓	500	`exa`	`ipopt`	107.425	20	771.008497	min
✓	500	`exa`	`madnlp`	105.369	25	771.008498	min	✓
✓	500	`jump`	`ipopt`	226.803	20	771.008497	min
✓	500	`jump`	`madnlp`	301.518	25	771.008498	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	766.685	20	771.008007	min
✓	1000	`adnlp`	`madnlp`	1074.234	23	771.008010	min
✓	1000	`exa`	`ipopt`	221.705	20	771.008007	min
✓	1000	`exa`	`madnlp`	205.497	23	771.008010	min	✓
✓	1000	`jump`	`ipopt`	567.387	20	771.008007	min
✓	1000	`jump`	`madnlp`	686.016	23	771.008010	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	2457.990	26	771.007873	min
✓	2000	`adnlp`	`madnlp`	2218.980	24	771.007877	min
✓	2000	`exa`	`ipopt`	718.367	26	771.007873	min
✓	2000	`exa`	`madnlp`	549.457	24	771.007877	min	✓
✓	2000	`jump`	`ipopt`	1646.167	26	771.007873	min
✓	2000	`jump`	`madnlp`	1709.058	24	771.007877	min

ℹ️ Log

Benchmarks results:

┌─ Problem: balanced_field
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  72.376 ms | iters: 17    | obj: 7.710114e+02  (min) | CPU:  34.27 KiB
│  │  ✓ | adnlp    | time:  96.244 ms | iters: 17    | obj: 7.710114e+02  (min) | CPU:  23.01 MiB
│  │  ✓ | exa      | time:  39.684 ms | iters: 17    | obj: 7.710114e+02  (min) | CPU: 129.05 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 226.803 ms | iters: 20    | obj: 7.710085e+02  (min) | CPU:  39.84 KiB
│  │  ✓ | adnlp    | time: 311.994 ms | iters: 20    | obj: 7.710085e+02  (min) | CPU:  66.33 MiB
│  │  ✓ | exa      | time: 107.425 ms | iters: 20    | obj: 7.710085e+02  (min) | CPU: 242.52 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 567.387 ms | iters: 20    | obj: 7.710080e+02  (min) | CPU:  39.84 KiB
│  │  ✓ | adnlp    | time: 766.685 ms | iters: 20    | obj: 7.710080e+02  (min) | CPU: 132.41 MiB
│  │  ✓ | exa      | time: 221.705 ms | iters: 20    | obj: 7.710080e+02  (min) | CPU: 425.89 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   1.646 s  | iters: 26    | obj: 7.710079e+02  (min) | CPU:  52.17 KiB
│  │  ✓ | adnlp    | time:   2.458 s  | iters: 26    | obj: 7.710079e+02  (min) | CPU: 340.26 MiB
│  │  ✓ | exa      | time: 718.367 ms | iters: 26    | obj: 7.710079e+02  (min) | CPU: 799.88 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:  99.835 ms | iters: 23    | obj: 7.710114e+02  (min) | CPU:  33.60 MiB
│  │  ✓ | adnlp    | time: 148.208 ms | iters: 23    | obj: 7.710114e+02  (min) | CPU:  34.39 MiB
│  │  ✓ | exa      | time:  39.870 ms | iters: 23    | obj: 7.710114e+02  (min) | CPU:   5.94 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time: 301.518 ms | iters: 25    | obj: 7.710085e+02  (min) | CPU:  85.66 MiB
│  │  ✓ | adnlp    | time: 366.933 ms | iters: 25    | obj: 7.710085e+02  (min) | CPU:  91.24 MiB
│  │  ✓ | exa      | time: 105.369 ms | iters: 25    | obj: 7.710085e+02  (min) | CPU:  14.32 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 686.016 ms | iters: 23    | obj: 7.710080e+02  (min) | CPU: 169.02 MiB
│  │  ✓ | adnlp    | time:   1.074 s  | iters: 23    | obj: 7.710080e+02  (min) | CPU: 168.74 MiB
│  │  ✓ | exa      | time: 205.497 ms | iters: 23    | obj: 7.710080e+02  (min) | CPU:  27.23 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:   1.709 s  | iters: 24    | obj: 7.710079e+02  (min) | CPU: 329.95 MiB
│  │  ✓ | adnlp    | time:   2.219 s  | iters: 24    | obj: 7.710079e+02  (min) | CPU: 349.57 MiB
│  │  ✓ | exa      | time: 549.457 ms | iters: 24    | obj: 7.710079e+02  (min) | CPU:  54.63 MiB
│  └─
└─