benchmarks: Initial DirectTrajOpt benchmark suite (Ipopt vs MadNLP)

[jack-champagne]

Summary

Initial benchmarking infrastructure for DirectTrajOpt.jl comparing Ipopt and MadNLP solvers on the feat/madnlp-integration branch.

Depends on: HarmoniqsBenchmarks.jl (new shared package — needs to be created in the org)

What's included

• `benchmark/Project.toml` — Benchmark environment with HarmoniqsBenchmarks, BenchmarkTools, TestItems, MadNLP
• `benchmark/benchmarks.jl` — Three `@testitem` suites:
  • Evaluator micro-benchmarks (bilinear N=51) — BenchmarkTools timing for each MOI eval function
  • Ipopt vs MadNLP macro-benchmark (bilinear N=51) — full-solve comparison
  • Memory scaling study — sweep N ∈ {25, 51, 101} × state_dim ∈ {4, 8, 16}
• `docs/superpowers/specs/2026-04-15-benchmarking-design.md` — overall architecture
• `docs/superpowers/specs/2026-04-15-altissimo-gpu-benchmarks-design.md` — 3-way GPU benchmark design
• `docs/superpowers/plans/2026-04-15-benchmarking-infrastructure.md` — implementation plan

Preliminary Results

Ipopt vs MadNLP (bilinear N=51)

Solver	Wall time	Allocations
Ipopt	8.52s	3.4 GB
MadNLP	5.75s (33% faster)	1.9 GB (43% less)

Micro-benchmark hotspot

`eval_hessian_lagrangian` is the clear optimization target — 12.7ms median, 73K allocations, 68MB per call.

Test plan

• Run `julia --project=benchmark -e 'using TestItemRunner; @run_package_tests(benchmark)'` — all 3 benchmarks produce JLD2 artifacts
• Verify results load correctly via `load_results` / `load_micro_results`
• Review preliminary Ipopt vs MadNLP timing numbers

🤖 Generated with Claude Code