How do I install the Lagrangian Core skill?

Run npx skillmds@latest add sliky1/lagrangian-core-3 in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

Is Lagrangian Core safe to use?

This skill has not completed SkillMD's automated safety review yet. SkillMD never runs a skill's scripts for you; review the SKILL.md before installing.

Which AI agents work with Lagrangian Core?

This skill is tagged as working with Claude Code, Claude.ai, OpenAI Codex. SKILL.md is an open format, so most agents that read a skills directory can load it too.

Is Lagrangian Core free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under MIT.

Who published Lagrangian Core?

Sliky1 (@sliky1) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Lagrangian Core by sliky1 — Agent Skill

Name: Lagrangian Core
Author: Sliky1

Lagrangian Core

Augmented Lagrangian for constrained optimization. Handles convex QP, smooth NLP, non-convex NLP, distributed ADMM, Safe RL, multi-objective. Trigger on: constrained optimization, KKT, ALM, ADMM, safe constraints, Pareto front, multi-objective. Also trigger for: shadow prices, sensitivity analysis, infeasibility diagnosis.

Sliky1 7b96f8b 2.0 KB Updated Sep 17, 2026

File contents

Lagrangian Core Skill — v0.5.0

能力边界

输出模式: MINIMAL | STANDARD(默认) | VERBOSE

Step -1 — 预检 (4项并行)

变量类型 2. 约束可行性 3. 问题规模 4. 量纲一致性 HALT条件 → 立即停止，输出错误码

Step 0 — 澄清

模糊点→单轮确认；贝叶斯信号→HALT "请调用贝叶斯Skill"

Step 3 — 稀疏JSON通道

{"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 5 — 求解路由

safe_rl+adversarial    → cos_thresh=0.15, window=15
multi_obj+adversarial  → max_repair=3, repair_freq=8
non_convex+adversarial → ALM(n_starts=10, uniform_random)
non_convex+normal      → ALM(n_starts=10, warm_start=cache)
convex_qp/smooth_nlp   → standard_solver
distributed            → ADMM

Step 6 — 影子价格

只输出活跃约束(影子价格>0)

Step 7 — 输出

STANDARD: 最优解(一行) → 约束状态(仅活跃) → 关键瓶颈(一句) VERBOSE: STANDARD + Steps 3-6 JSON

失败处理

{"status":"FAILED","error_code":"INFEASIBLE|BAD_PARAMS|AMBIGUOUS|SOLVER_FAIL",
 "reason":"<一行>","recovery":"<修复建议>"}

Forbidden Behaviors

❌ Steps 1-6输出自然语言 | ❌ Step 7输出JSON ❌ 语言边界直接HALT | ❌ 失败后输出散文 ❌ FIX-16: cos_thresh>0.20或window<15

---name: lagrangian-core-3description: Augmented Lagrangian for constrained optimization. Handles convex QP, smooth NLP, non-convex NLP, distributed ADMM, Safe RL, multi-objective. Trigger on: constrained optimization, KKT, ALM, ADMM, safe constraints, Pareto front, multi-objective. Also trigger for: shadow prices, sensitivity analysis, infeasibility diagnosis.license: MIT---# Lagrangian Core Skill — v0.5.0## 能力边界支持: 凸QP | 光滑NLP | 非凸NLP | 分布式ADMM | Safe RL | 多目标协同: 检测贝叶斯/统计成分→HALT并建议调用对应Skill不支持: 纯贝叶斯 | 纯统计检验 | MIP输出模式: MINIMAL | STANDARD(默认) | VERBOSE## Step -1 — 预检 (4项并行)1. 变量类型 2. 约束可行性 3. 问题规模 4. 量纲一致性HALT条件 → 立即停止，输出错误码## Step 0 — 澄清模糊点→单轮确认；贝叶斯信号→HALT "请调用贝叶斯Skill"## 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 5 — 求解路由```safe_rl+adversarial → cos_thresh=0.15, window=15multi_obj+adversarial → max_repair=3, repair_freq=8non_convex+adversarial → ALM(n_starts=10, uniform_random)non_convex+normal → ALM(n_starts=10, warm_start=cache)convex_qp/smooth_nlp → standard_solverdistributed → ADMM```## Step 6 — 影子价格只输出活跃约束(影子价格>0)## Step 7 — 输出STANDARD: 最优解(一行) → 约束状态(仅活跃) → 关键瓶颈(一句)VERBOSE: STANDARD + Steps 3-6 JSON## 失败处理```json{"status":"FAILED","error_code":"INFEASIBLE|BAD_PARAMS|AMBIGUOUS|SOLVER_FAIL", "reason":"<一行>","recovery":"<修复建议>"}```## Forbidden Behaviors❌ Steps 1-6输出自然语言 | ❌ Step 7输出JSON❌ 语言边界直接HALT | ❌ 失败后输出散文❌ FIX-16: cos_thresh>0.20或window<15

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