docs: rename lp-qp-milp doc containers to numerical-optimization

[rgsl888prabhu]

Summary

Renames the grouping documentation directories and consolidated files that bundle LP + QP + MILP together to numerical-optimization, and updates the corresponding section titles, so adding a new problem type in the future no longer forces renaming/relabeling these containers.

File/dir renames

Old	New
docs/.../cuopt-c/lp-qp-milp/	docs/.../cuopt-c/numerical-optimization/
docs/.../cuopt-python/lp-qp-milp/	docs/.../cuopt-python/numerical-optimization/
lp-qp-milp-settings.rst	numerical-optimization-settings.rst
lp-qp-milp-c-api.rst	numerical-optimization-c-api.rst
lp-qp-milp-api.rst	numerical-optimization-api.rst
lp-qp-milp-examples.rst	numerical-optimization-examples.rst

Renames use git mv so file history is preserved. All toctree entries and :doc: cross-references are updated.

Section title updates (LP/QP/MILP -> Numerical Optimization)

• Numerical Optimization Settings
• Numerical Optimization API Reference (Python)
• Numerical Optimization Examples (Python)
• cuOpt Numerical Optimization C API Reference
• numerical-optimization/index.rst titles (Python & C)

Scope / out of scope

• In scope: the cross-cutting grouping containers and their all-three section titles.
• Left as-is (per-type / contrast): lp-qp-features.rst, milp-features.rst, per-type example pages and code (simple_lp_example.c, etc.), single-type headers (MILP Features, Linear Programming (LP), ...), toctree captions, and the gRPC routing-vs-numeric contrast labels.
• Follow-up: skill files under skills/ still reference the old lp-qp-milp doc paths; these will be updated separately, one skill at a time, after this merges.

Verification

• Zero remaining lp-qp-milp occurrences under docs/.
• All renamed toctree/:doc: targets confirmed to exist on disk.
• RST title underline lengths validated (>= title length) for all updated headers.

🤖 Generated with Claude Code

[coderabbitai]

Walkthrough

Documentation references and toctree entries are updated to use numerical-optimization naming instead of lp-qp-milp across C, Python, CLI, gRPC, Server, and shared settings documentation.

Changes

Documentation path migration to numerical-optimization naming

Layer / File(s)	Summary
C API documentation structure and content updates docs/cuopt/source/cuopt-c/index.rst, docs/cuopt/source/cuopt-c/numerical-optimization/index.rst, docs/cuopt/source/cuopt-c/numerical-optimization/lp-qp-example.rst, docs/cuopt/source/cuopt-c/numerical-optimization/milp-examples.rst, docs/cuopt/source/cuopt-c/numerical-optimization/numerical-optimization-c-api.rst	C API index, numerical-optimization index, examples, and C API reference updated to reference numerical-optimization naming and settings links.
Python API documentation structure updates docs/cuopt/source/cuopt-python/index.rst, docs/cuopt/source/cuopt-python/numerical-optimization/index.rst, docs/cuopt/source/cuopt-python/numerical-optimization/numerical-optimization-api.rst, docs/cuopt/source/cuopt-python/numerical-optimization/numerical-optimization-examples.rst	Python API index and nested numerical-optimization pages updated to reference numerical-optimization-api and numerical-optimization-examples and renamed headings.
Cross-API documentation reference updates docs/cuopt/source/cuopt-cli/quick-start.rst, docs/cuopt/source/cuopt-grpc/examples.rst, docs/cuopt/source/cuopt-grpc/quick-start.rst, docs/cuopt/source/cuopt-server/examples/lp-examples.rst, docs/cuopt/source/cuopt-server/server-api/index.rst, docs/cuopt/source/numerical-optimization-settings.rst, docs/cuopt/source/transition.rst	CLI, gRPC, Server, transition guide, and shared settings docs updated to point to numerical-optimization-settings and the new numerical-optimization C API doc paths.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Suggested labels

non-breaking, improvement

Suggested reviewers

• tmckayus
• Iroy30

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly and concisely summarizes the main change: renaming documentation containers from 'lp-qp-milp' to 'numerical-optimization', which is exactly what the changeset implements.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.

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✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch docs/rename-lp-qp-milp-to-numerical-optimization

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