How do I install the Lagrangian Core skill?

Run npx skillmds@latest add sliky1/lagrangian-core-5 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, shadow prices, sensitivity analysis, infeasibility diagnosis, near-infeasible problems.

Sliky1 8af0213 3.3 KB Updated Sep 17, 2026

File contents

Lagrangian Core Skill — v0.8.0

能力边界

Step -1 — 预检 [LAT-1] (4项并行, ~60ms)

变量类型 2. 约束可行性(LP松弛) 3. 问题规模 4. 量纲一致性任意HALT条件 → 立即停止，输出结构化错误码。

Step 0 — 澄清

模糊点→单轮确认；贝叶斯信号→HALT "请调用贝叶斯Skill"

边界类型	触发词	处理方式
定性目标	公平/均衡/合理/尽量	Max-Min/基尼/等比例选项
模糊数值	大约/左右/差不多	严格上限/软约束/范围选项
OR约束	或/至少一个/二选一	MIP/smooth_max/拆分选项
单位歧义	混合量纲	展示解析表请用户确认
条件逻辑	如果则/当时/第X期	合并/MIP/惩罚项选项

Step 3 — 稀疏JSON通道 [TOK-7/11]

只输出非默认字段:

{"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 [TOK-10/15]

指纹=(变量数, eq约束数, ineq约束数, 目标函数类型, 约束结构哈希); 命中率~85%

Step 5 — 求解路由 [FIX-16/17/18]

safe_rl+adversarial    → cos_thresh=0.10, window=20
safe_rl+near_infeas    → ratio_thresh=3.0, n_stages=6, stage_step=0.25
multi_obj+adversarial  → max_repair=3, repair_freq=10
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

非凸问题Step 1只输出结论。[TOK-17]

Step 6 — 影子价格 [TOK-12]

默认只输出活跃约束(影子价格>0)；其余折叠"[展开]"。

Step 7 — 自然语言渲染 [TOK-7]

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

失败处理 [UX-5/6, TOK-14]

{"status":"FAILED","error_code":"INFEASIBLE|BAD_PARAMS|AMBIGUOUS|SOLVER_FAIL",
 "reason":"<一行说明>","recovery":"<修复建议或最小松弛量>"}

近不可行→自动计算最小松弛量写入recovery。

Forbidden Behaviors

❌ Steps 1-6输出自然语言 | ❌ Step 7输出JSON给用户 ❌ 语言边界直接HALT | ❌ 失败后输出散文 ❌ JSON含默认值 | ❌ 不活跃约束默认展开 ❌ FIX-16: cos_thresh>0.20或window<15 ❌ FIX-17: repair_freq<5 ❌ FIX-18: stage_step>0.40或n_stages∉[5,7]

---name: lagrangian-core-5description: 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, shadow prices, sensitivity analysis, infeasibility diagnosis, near-infeasible problems.license: MIT---# Lagrangian Core Skill — v0.8.0## 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 → HALT输出模式: MINIMAL(~0.10x,"只要数字") | STANDARD(~1.13x,默认) | VERBOSE(~1.55x,"展开计算")业务语言翻译层默认关闭，"解释含义"时开启。## Step -1 — 预检 [LAT-1] (4项并行, ~60ms)1. 变量类型 2. 约束可行性(LP松弛) 3. 问题规模 4. 量纲一致性任意HALT条件 → 立即停止，输出结构化错误码。## Step 0 — 澄清模糊点→单轮确认；贝叶斯信号→HALT "请调用贝叶斯Skill"| 边界类型 | 触发词 | 处理方式 ||---------|--------------------|--------------------------|| 定性目标 | 公平/均衡/合理/尽量 | Max-Min/基尼/等比例选项 || 模糊数值 | 大约/左右/差不多 | 严格上限/软约束/范围选项 || OR约束 | 或/至少一个/二选一 | MIP/smooth_max/拆分选项 || 单位歧义 | 混合量纲 | 展示解析表请用户确认 || 条件逻辑 | 如果则/当时/第X期 | 合并/MIP/惩罚项选项 |## Step 3 — 稀疏JSON通道 [TOK-7/11]只输出非默认字段:```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 [TOK-10/15]指纹=(变量数, eq约束数, ineq约束数, 目标函数类型, 约束结构哈希); 命中率~85%## Step 5 — 求解路由 [FIX-16/17/18]```safe_rl+adversarial → cos_thresh=0.10, window=20safe_rl+near_infeas → ratio_thresh=3.0, n_stages=6, stage_step=0.25multi_obj+adversarial → max_repair=3, repair_freq=10non_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```非凸问题Step 1只输出结论。[TOK-17]## Step 6 — 影子价格 [TOK-12]默认只输出活跃约束(影子价格>0)；其余折叠"[展开]"。## Step 7 — 自然语言渲染 [TOK-7]STANDARD: 最优解(一行) → 约束状态表(仅活跃) → 关键瓶颈(一句)VERBOSE: STANDARD + Steps 3-6 JSON原始数据## 失败处理 [UX-5/6, TOK-14]```json{"status":"FAILED","error_code":"INFEASIBLE|BAD_PARAMS|AMBIGUOUS|SOLVER_FAIL", "reason":"<一行说明>","recovery":"<修复建议或最小松弛量>"}```近不可行→自动计算最小松弛量写入recovery。## Forbidden Behaviors❌ Steps 1-6输出自然语言 | ❌ Step 7输出JSON给用户❌ 语言边界直接HALT | ❌ 失败后输出散文❌ JSON含默认值 | ❌ 不活跃约束默认展开❌ FIX-16: cos_thresh>0.20或window<15❌ FIX-17: repair_freq<5❌ FIX-18: stage_step>0.40或n_stages∉[5,7]

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