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feat: add Levenberg–Marquardt and Goldfarb–Idnani active-set QP - #358

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feat: add Levenberg–Marquardt and Goldfarb–Idnani active-set QP#358
gabrielfrasantos merged 3 commits into
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claude/brave-einstein-5nj7y6

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@gabrielfrasantos gabrielfrasantos commented Oct 23, 2026 •
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Summary

Tier 4 of the roadmap items added in #353. With this PR every spec from #353 is deployed and removed from roadmap/.

  • feat: add pid absolute #64 Levenberg–Marquardt (optimization): bounded-iteration damped Gauss–Newton over a LeastSquaresProblem interface (residual, Jacobian w.r.t. a local increment, retraction x ⊕ δ). Damping comes from a DampingPolicy interface, with ConstantDamping provided (λ = 0 is Gauss–Newton). Each step solves the smaller normal system with LU and can be capped by maxStep. A singular system stops the solve instead of dividing by zero.
  • Fix sonarqube coverage #65 Active-set QP (solvers): Goldfarb–Idnani dual method in Powell's J = L⁻ᵀQ / R form, with Givens add/drop updates. It needs no feasible start and reports Optimal / Infeasible / NotPositiveDefinite / IterationLimit. QuadraticProgram is specialised for zero equalities or zero inequalities, since math::Matrix has no zero-size form.

Spec corrections (float32)

  • QP linear dependence: a constraint counts as dependent on the active set when ‖d₂‖ ≤ 1e-5·‖d‖ (relative), not ‖z‖ ≤ ε (absolute). With the absolute test, 73 of 3000 infeasible random problems were reported Optimal after a wild step. The relative test agrees with a brute-force KKT enumeration on all of them.
  • LM Rosenbrock test: tolerance is 1e-4 instead of 1e-5. cond(JJᵀ) ≈ 4600 there, so float32 Gauss–Newton ends its two exact steps at ‖r‖ ≈ 1e-5, right on the spec's threshold.

Verification

  • Unit tests pass on host GCC and Clang.
  • The QP was prototyped in numpy, then the C++ solver was cross-checked on 3000 random problems of shapes (2,1,2), (2,0,4) and (4,2,8), with duplicated, negated, dependent and badly scaled rows. Every optimal x matches the oracle to ≈1e-4 relative; scaled KKT residual ≤ 4.4e-6, primal infeasibility ≤ 1.2e-5, and no negative inequality multipliers. This also exercises the multi-constraint drop path, which the spec's enumerated tests do not reach.
  • Coverage with template instances merged: LM 100%, QP 91%.

Stack

Base: main (#355 and #357 merged). This is the last PR of the stack.

Generated by Claude Code

@gabrielfrasantos
gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from e31c9cb to b4f9aad Compare October 23, 2026 16:26
@gabrielfrasantos
gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6 branch from b2eaa24 to 1f304dc Compare October 23, 2026 16:26
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✅⚠️MegaLinter analysis: Success with warnings

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Detailed Issues

⚠️ SPELL / lychee - 23 errors 
📝 Summary
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🔀 Redirected.....151
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⛔ Unsupported.....23

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[ERROR] file:///releases/latest (at 39:14) | File not found. Check if file exists and path is correct
[404] https://embedded-pro.github.io/embedded-dsp-control/ (at 38:1) | Rejected status code: 404 Not Found

Hint: Followed 151 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
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⚠️ MARKDOWN / markdownlint - 163 errors 
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doc/solvers/DampedPseudoInverse.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 531]
doc/solvers/DampedPseudoInverse.md:89:401 error MD013/line-length Line length [Expected: 400; Actual: 581]
doc/solvers/JacobiEigenSolver.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 443]
doc/solvers/JacobiEigenSolver.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 609]
doc/solvers/JacobiEigenSolver.md:45:401 error MD013/line-length Line length [Expected: 400; Actual: 427]
doc/solvers/RungeKuttaIntegrators.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 509]
doc/solvers/SpectralRadius.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 665]
doc/solvers/SymplecticIntegrators.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 486]
doc/solvers/SymplecticIntegrators.md:35:401 error MD013/line-length Line length [Expected: 400; Actual: 476]
doc/solvers/SymplecticIntegrators.md:63:401 error MD013/line-length Line length [Expected: 400; Actual: 431]
doc/windowing/window.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 415]
README.md:1 error MD041/first-line-heading/first-line-h1 First line in a file should be a top-level heading [Context: "[![Quality Gate Status](https:..."]
README.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 442]
README.md:17:401 error MD013/line-length Line length [Expected: 400; Actual: 507]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 21224)

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@gabrielfrasantos
gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from b4f9aad to c3a69f1 Compare October 23, 2026 16:28
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6 branch from 1f304dc to c8bee9e Compare October 23, 2026 16:28
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from c3a69f1 to cc806a4 Compare October 23, 2026 16:31
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from a445fb3 to cef9e71 Compare October 23, 2026 17:07
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6 branch from 3d3b32e to a586ab5 Compare October 23, 2026 17:07
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Merged
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from cef9e71 to 920b43d Compare October 23, 2026 17:47
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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6 branch from a586ab5 to 7a73f5e Compare October 23, 2026 17:47
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Merged
Base automatically changed from claude/brave-einstein-5nj7y6-tier3 to main October 23, 2026 17:52
claude added 3 commits October 23, 2026 17:52
@claude
feat(optimization): add Levenberg–Marquardt with retraction and dampi…
599a35e 
…ng policy

Deploy roadmap item 64: bounded-iteration damped Gauss–Newton over a
LeastSquaresProblem interface (residual, Jacobian w.r.t. a local
increment, retraction x ⊕ δ) and a DampingPolicy interface
(ConstantDamping; λ = 0 is Gauss–Newton). Each step solves the smaller
normal system with LU, can be capped by maxStep, and a singular
system stops the solve unconverged instead of dividing by zero.

The Rosenbrock test uses tolerance 1e-4 instead of the spec's 1e-5:
cond(JJᵀ) ≈ 4600 there, so float32 Gauss–Newton ends its two exact
steps at ‖r‖ ≈ 1e-5, right on the spec's threshold.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5
@claude
feat(solvers): add Goldfarb–Idnani dual active-set QP
af4b57f 
Deploy roadmap item 65: dense strictly convex QP with equality and
inequality constraints, using the Goldfarb–Idnani dual method in
Powell's J = L⁻ᵀQ / R form with Givens add/drop updates. It needs no
feasible start, adds equalities first, then the most violated
inequality, and reports Optimal / Infeasible / NotPositiveDefinite /
IterationLimit. QuadraticProgram is specialised for zero equalities
or zero inequalities, since math::Matrix has no zero-size form.

Change from the spec: a constraint counts as linearly dependent on the
active set when ‖d₂‖ ≤ 1e-5·‖d‖ (relative), not when ‖z‖ ≤ ε. In
float32 the absolute test reported 73 of 3000 infeasible random
problems as optimal after a wild step. The relative test agrees with a
brute-force KKT enumeration on all of them.

The C++ solver was cross-checked on 3000 random problems of shapes
(2,1,2), (2,0,4) and (4,2,8), including duplicated, negated, dependent
and badly scaled rows: optimal x matches the oracle to ≈1e-4
relative, scaled KKT residual ≤ 4.4e-6, no negative inequality
multipliers.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5
@claude
docs: align markdown tables
f02d204 
Apply markdown-table-formatter's layout to the tables this tier adds
or edits, as suggested by MegaLinter.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5
@gabrielfrasantos
gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6 branch from 7a73f5e to f02d204 Compare October 23, 2026 17:52
@sonarqubecloud

sonarqubecloud Bot commented Oct 23, 2026

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Quality Gate Passed Quality Gate passed

Issues
1 New issue
0 Accepted issues

Measures
0 Security Hotspots
89.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

@gabrielfrasantos
gabrielfrasantos merged commit 1f6d717 into main Oct 23, 2026
14 checks passed
@gabrielfrasantos
gabrielfrasantos deleted the claude/brave-einstein-5nj7y6 branch October 23, 2026 17:59
@embedded-releaser-app embedded-releaser-app Bot mentioned this pull request Oct 23, 2026
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2 participants

@gabrielfrasantos @claude