V0.7.0

Skill Sliky1/lagrangian-skills/archive/v0.7.0

Agent Skill for constrained optimization via ALM/ADMM/KKT — with adversarial guards, COOP cross-skill protocol, and 20k-sim validated parameters

Install

npx -y skills add Sliky1/lagrangian-skills --skill v0.7.0

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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.

The file declares its own license as MIT. That is the author’s claim about this one file, and it is not the same thing as the license GitHub reports for the repository, which is listed with the other numbers below.

SKILL.md

2.6 KB, as published. Nobody here has run it

Lagrangian Core Skill — v0.7.0

能力边界

Step -1 — 预检 [LAT-1] (4项并行)

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"

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 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, 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    [FIX-16]
safe_rl+near_infeas    → ratio_thresh=3.0, n_stages=6, stage_step=0.25  [FIX-18]
multi_obj+adversarial  → max_repair=3, repair_freq=10  [FIX-17]
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

默认只输出活跃约束(影子价格>0)；其余折叠"[展开]"。

Step 7 — 输出

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

{"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 ❌ 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]