Add cuopt-multi-objective-exploration skill (Pareto frontier)

[cafzal]

Description

Adds cuopt-multi-objective-exploration — a concept skill for problems with two or more objectives and no fixed weighting, where the user wants to see the tradeoff instead of accepting one weighted answer. It turns repeated single-objective cuOpt solves into a Pareto frontier (payoff table → ε-constraint / weighted-sum sweep → filter dominated) and supplies the discipline to read it: exchange rates, knee points, deferring the final choice. It adds no solver features and invents no API — it sits above the api-* and formulation skills, and is linked from the goal-programming pattern in cuopt-numerical-optimization-formulation (which already covers the fixed-priority case).

cuOpt-specific correctness points

• ε-constraining is most natural on linear objectives, so a quadratic objective (risk xᵀΣx) can simply stay the objective. A convex one can also be ε-constrained directly — cuOpt routes xᵀQx ≤ ε through the barrier solver as a second-order cone (add_quadratic_constraint, inequality only), though SOCP support is beta.
• PDLP warm-start is LP-only; MILP frontier points are optimal to the gap you set, since each solve gets a time limit.
• A hard constraint (coverage floor, budget, fairness cap) is often a latent objective — promote it to a swept ε-constraint (when its level was an assumption, not a firm limit).

User testing

Used the skill to enrich two existing examples and confirmed it drove the right calls — companion PR NVIDIA/cuopt-examples#151:

• Workforce (MILP) — promoted two hard constraints into tradeoffs (coverage → cost vs. coverage; the max_shifts cap → cost vs. fairness), chose ε-constraint over weighted-sum, anchored objective ranges, filtered dominated points, capped each solve, and reported no MILP duals.
• Portfolio (QP) — recognized the base notebook's hand-coded target-return loop as ε-constraint and added what it omits: the return-constraint dual (shadow price d(variance)/d(return)), with the PDLP-tolerance caveat.

The skill drives the method; runnable code still needs cuopt-numerical-optimization-api-python plus the worked notebooks, which are Colab-GPU validated (T4, clean end-to-end).

Validation & gating

Registered in AGENTS.md + marketplace.json; ci/utils/validate_skills.sh passes. The contribution is SKILL.md + evals/evals.json — BENCHMARK.md, the skill card, and skill.oms.sig are generated by the NVSkills onboarding pipeline. The official NVSkills-Eval is the gate (PENDING).

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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[rgsl888prabhu]

@cafzal Thank you for the draft PR, do you have access to push PR branch to main repo? Currently there is a requirement for skill related PRs to be made available in main repo to trigger CI pipe line.

Once you have done that, pipeline will validate and eval. It will also create BENCHMARK.md and skill card.

[cafzal]

Thank you for the draft PR, do you have access to push PR branch to main repo? Currently there is a requirement for skill related PRs to be made available in main repo to trigger CI pipe line.

Once you have done that, pipeline will validate and eval. It will also create BENCHMARK.md and skill card.

@rgsl888prabhu I don't have write access to NVIDIA/cuopt (push: false), so I've been working from my own fork.

Could you either:

1. Push this PR's branch to the main repo on your end so the skill CI can run; or
2. Add me as a collaborator (write access) and I'll push it up.

Either works for me. Thanks.