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nonlinear-solvers

Maintainer FreedomIntelligence · Last updated April 1, 2026

Select and configure nonlinear solvers for f(x)=0 or min F(x). Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.

OpenClawNanoClawAnalysisWritingnonlinear-solvers📊 data science & toolscomputational simulation & ontologyselect

Original source

FreedomIntelligence/OpenClaw-Medical-Skills

https://github.com/FreedomIntelligence/OpenClaw-Medical-Skills/tree/main/skills/nonlinear-solvers

Maintainer: FreedomIntelligence
License: MIT
Last updated: April 1, 2026

Skill Snapshot

Key Details From SKILL.md

2 min

Key Notes

Provide a universal workflow to select a nonlinear solver, configure globalization strategies, and diagnose convergence for root-finding, optimization, and least-squares problems.
python3 scripts/solver_selector.py --size 50000 --smooth --memory-limited --json.

Source Doc

Excerpt From SKILL.md

Requirements

Python 3.8+
NumPy (for Jacobian diagnostics)
SciPy (optional, for advanced analysis)

Inputs to Gather

Input	Description	Example
Problem type	Root-finding, optimization, least-squares	`root-finding`
Problem size	Number of unknowns	`n = 10000`
Jacobian availability	Analytic, finite-diff, unavailable	`analytic`
Jacobian cost	Cheap or expensive to compute	`expensive`
Constraints	None, bounds, equality, inequality	`none`
Smoothness	Is objective/residual smooth?	`yes`
Residual history	Sequence of residual norms	`1,0.1,0.01,...`

Script Outputs (JSON Fields)

Script	Key Outputs
`scripts/solver_selector.py`	`recommended`, `alternatives`, `notes`
`scripts/convergence_analyzer.py`	`converged`, `convergence_type`, `estimated_rate`, `diagnosis`
`scripts/jacobian_diagnostics.py`	`condition_number`, `jacobian_quality`, `rank_deficient`
`scripts/globalization_advisor.py`	`strategy`, `line_search_type`, `trust_region_type`, `parameters`
`scripts/residual_monitor.py`	`patterns_detected`, `alerts`, `recommendations`
`scripts/step_quality.py`	`ratio`, `step_quality`, `accept_step`, `trust_radius_action`

Use cases

Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.

Not for

Do not rely on this catalog entry alone for installation or maintenance details.

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