# Lagrangian Core

> Augmented Lagrangian for constrained optimization. Handles convex QP, smooth NLP, non-convex NLP, distributed ADMM. Trigger on: constrained optimization, KKT, Lagrange multipliers, ALM, ADMM, multi-start, penalty methods.

- Skill: `sliky1/lagrangian-core-2` (Agent Skill)
- Install (CLI): `npx skillmds@latest add sliky1/lagrangian-core-2`
- Raw SKILL.md: https://api.skillmd.com/api/skills/sliky1/lagrangian-core-2/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: Sliky1 (https://skillmd.com/u/sliky1)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/sliky1/lagrangian-core-2

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# Lagrangian Core Skill — v0.3.0

## 能力边界
支持: 凸QP | 光滑NLP | 非凸NLP(multi-start) | 分布式ADMM
不支持: Safe RL | 多目标 | 贝叶斯混合

## 方法路由
```
convex_qp/smooth_nlp → standard_solver
non_convex           → ALM(n_starts=5, uniform_random)
distributed          → ADMM
```

## Step 3 — 稀疏JSON通道
```json
{"step":3,"type":"augmented_lagrangian",
 "formula":"L_ρ=f(x)+Σλ·h(x)+Σμ·g(x)+ρ/2·||h||²",
 "multipliers":{"lambda":[0.0],"mu":[0.0]},
 "penalty":{"rho_init":1.0,"update_rule":"×1.5 if ||h||>tol"}}
```

## Step 4 — KKT验证
缓存指纹=(变量数, eq约束数, ineq约束数, 目标函数类型)

## Step 7 — 输出
最优解(一行) → 约束状态 → KKT残差

## Forbidden Behaviors
❌ Steps 1-6输出自然语言
❌ 失败后输出散文