Note dual/sensitivity support per problem type in formulation skill

[cafzal]

Description

Adds a per-problem-type dual / sensitivity capability note to the concepts-only cuopt-numerical-optimization-formulation skill, so the agent guides users correctly on what cuOpt exposes after a solve:

• LP — shadow prices (constraint duals) + reduced costs
• MILP — none (integer optima are not continuous)
• QP — shadow prices + reduced costs

Two edits: a Duals / sensitivity row in the LP/MILP/QP comparison table, and a short post-solve note giving the decision meaning — shadow price = where to invest (marginal objective gain from relaxing a binding constraint) and reduced cost = near-miss (how far a left-out option must improve before it enters the solution). As a concepts skill it states what's supported per type and what it means, and defers how to read them to the language-specific API skills (no API symbols inlined).

Why. Surfaced from real integration use — wiring solver-exact sensitivity/explainability into a downstream multi-objective decision layer. The formulation skill covered how to formulate but not which problem types yield sensitivity information, which is exactly what a user needs before relying on it (e.g. not expecting duals off a MILP).

The note also reflects the review feedback on #1355: a concepts skill carries no maturity ("beta") labels and no specific API symbols — both drift out of date, with no CI to catch the staleness.

Validation & gating. ci/utils/validate_skills.sh passes (skill structure, marketplace manifest, AGENTS.md references). The NVSkills-Eval pipeline — which also (re)generates BENCHMARK.md, the skill card, and the signature — is the gate and is pending: skills/** CI needs a maintainer and cannot be triggered from a fork branch.

Related.

• Add LP sensitivity analysis (duals + reduced costs) to the diet example cuopt-examples#154 — the diet LP duals example: a runnable worked case of the shadow-price / reduced-cost reading this note describes.
• Codebase-side sensitivity gaps (objective/RHS ranging; exposing variable/basis status) are tracked separately as [FEA] Expose basis / variable status on the LP solution (companion to reduced costs) #1394 and [FEA] LP sensitivity ranging (RHS + objective-coefficient ranges) #1395.

Checklist

• I am familiar with the Contributing Guidelines.
• Testing
  • New or existing tests cover these changes
  • Added tests
  • Created an issue to follow-up
  • NA
• Documentation
  • The documentation is up to date with these changes
  • Added new documentation
  • NA

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[coderabbitai]

📝 Walkthrough

Walkthrough

This PR adds educational documentation content to the "Identifying problem type" section, introducing a new comparison row for dual information and sensitivity analysis capabilities. The changes clarify that LP and QP support post-solve sensitivity metrics (dual values, shadow prices, reduced costs) while MILP formulations do not expose dual values.

Changes

Problem Type Identification Documentation

Layer / File(s)	Summary
Duals and sensitivity analysis comparison skills/cuopt-numerical-optimization-formulation/SKILL.md	Added new table row distinguishing LP, MILP, and QP dual availability, and expanded explanation of post-solve sensitivity analysis covering dual values, shadow prices, and reduced costs for LP/QP while explicitly stating MILP has no duals.

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~5 minutes

Suggested labels

non-breaking, improvement

Suggested reviewers

• rgsl888prabhu
• mlubin

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title 'Note dual/sensitivity support per problem type in formulation skill' directly and clearly describes the main change—documenting per-problem-type dual and sensitivity capabilities in the formulation skill.
Description check	✅ Passed	The description thoroughly explains the changes, motivation, and validation approach, covering what was added (dual/sensitivity rows and post-solve notes), why it matters (integration use case), and how it aligns with concepts-skill principles.
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.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[coderabbitai]

🧹 Nitpick comments (1)

skills/cuopt-numerical-optimization-formulation/SKILL.md (1)

1-40: Ensure merge gates for skills/ changes are satisfied.

Since this PR changes skills/**, please make sure a maintainer runs /nvskills-ci and the signature commit remains in the PR, and confirm all commits are DCO signed (git commit -s) before merge. As per coding guidelines, “PRs that change content under skills/ must be validated by NVSkills CI with maintainer /nvskills-ci comment before merge” and “Sign off all commits with DCO sign-off using git commit -s.”

🤖 Prompt for AI Agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@skills/cuopt-numerical-optimization-formulation/SKILL.md` around lines 1 -
40, This PR modifies content under skills/, so ensure a maintainer runs the
NVSkills CI validation by adding the "/nvskills-ci" comment and confirm the
signature commit remains in the PR; also verify every commit has a DCO sign-off
(use git commit -s for any missing sign-offs) before merging so the skill change
(SKILL.md) meets the merge gates.

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Nitpick comments:
In `@skills/cuopt-numerical-optimization-formulation/SKILL.md`:
- Around line 1-40: This PR modifies content under skills/, so ensure a
maintainer runs the NVSkills CI validation by adding the "/nvskills-ci" comment
and confirm the signature commit remains in the PR; also verify every commit has
a DCO sign-off (use git commit -s for any missing sign-offs) before merging so
the skill change (SKILL.md) meets the merge gates.

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Enterprise

Run ID: 1ea475be-1cda-4813-8328-a5465f2a9983

📥 Commits

Reviewing files that changed from the base of the PR and between 34465b2 and a401504.

📒 Files selected for processing (1)

• skills/cuopt-numerical-optimization-formulation/SKILL.md

[cafzal]

@rgsl888prabhu For visibility: Here's a minor skill addition to clarify dual/sensitivity support.

[rgsl888prabhu]

/ok to test a401504

[rgsl888prabhu]

/merge