V0.9.3
Agent Skill for constrained optimization via ALM/ADMM/KKT — with adversarial guards, COOP cross-skill protocol, and 20k-sim validated parameters
npx -y skills add Sliky1/lagrangian-skills --skill v0.9.3Assembled from the repository path, not quoted from the project. Check it against their README if it does not work.
One thing to look at
- 2 stars2 stars. Stars are a popularity signal and not a quality one, but at this level it is likely that nobody has read this closely except its author, and you would be relying on your own review.
What its author says it does
Copied from the file, not written here
Opinionated constrained optimization skill using Augmented Lagrangian Methods (ALM), ADMM, and KKT verification. Enforces step ordering, solver routing, feasibility checks, and adversarial guards that agents skip unprompted. Trigger on: constrained optimization, KKT conditions, Lagrange multipliers, ALM, ADMM, shadow prices, infeasibility diagnosis, safe RL constraints, multi-objective Pareto, Bayesian-optimization hybrids, or any problem with equality/inequality constraints. Also trigger for: sensitivity analysis, near-infeasible problems, non-convex landscapes, adversarial perturbations, or natural language problem specs.
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
6.4 KB, as published. Nobody here has run it
Lagrangian Core Skill — v0.9.3
Token <=1.13x | 成功率目标 98.5% | 文档 <=150行
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→抛出子任务→合并结果 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。
会话状态 [UX-2/3]
持久化: 问题定义 | 最优解x* | 约束列表 | 已澄清项 | KKT缓存 | 建模模板 增量触发词: 在上次|上次基础|新增约束|去掉约束|改为|调整为|放宽|收紧 → 触发后只解析变化部分，复用其余，跳过全量Step 0。
Step -1 — 预检 [LAT-1] (5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 5. 混合问题(COOP-1) 任意HALT条件 → 立即停止，输出结构化错误码。
[FIX-19] natural_lang+degenerate: Hessian条件数>1e6 → Tikhonov正则化(ε=1e-4)
[FIX-21v2] non_convex+adversarial起点: Halton序列; thresh=0.010, window=3, abandon=majority_vote
[FIX-22] non_convex+adversarial双层防护: Layer B (前置): ensemble_vote, quarantine=5 → safe_direction回退 Layer A (投影): adaptive_trust_region, proj_radius=0.10, restart_thresh=5 → 连续5步目标值劣化 → 重启+下一Halton起点 独立触发，执行顺序B→A；非此场景不启用。
[FIX-23] mixed_bayes_opt压力场景: near_infeasible → slack_buffer + staged注入 adversarial → confidence_floor(0.6) + staged注入
[FIX-24] Step 7退化标注: FIX-19 → "⚠️ 退化结构，已正则化(ε=1e-4)" FIX-22 → "⚠️ 对抗性鞍点：双层防护已激活" FIX-23 → "⚠️ COOP压力场景：{策略名}已激活"
Step 0 — 混合检测 + 批量澄清 [COOP-1, UX-2b/2c]
贝叶斯信号词: 先验|后验|似然|贝叶斯|概率分布|prior|posterior|likelihood 统计信号词: 均值|方差|回归|相关系数|假设检验 → 贝叶斯+优化: MIXED_BAYES_OPT → 抛出子任务(COOP-2) → 纯贝叶斯: HALT "请调用贝叶斯Skill"
批量澄清: ≥2个模糊点→合并单轮确认表(-0.12x)；澄清后增量更新解析树。
| 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-16~23]
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 → FIX-21v2 + FIX-22
natural_lang+degenerate → FIX-19
mixed_bayes+near_infeas → FIX-23(slack_buffer)
mixed_bayes+adversarial → FIX-23(confidence_floor)
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) → FIX标注 VERBOSE: STANDARD + Steps 3-6 JSON原始数据 非凸局部最优 → "已验证N起点，当前解优于X%起点。" [UX-8]
COOP-2/3 — 跨Skill协同
{"status":"AWAITING_EXTERNAL",
"subtask_for_external_skill":{"type":"bayesian_inference","input":"<子任务>",
"output_format":{"posterior_params":"dict","confidence":"float 0-1"}},
"merge_instruction":"posterior_params staged方式注入优化参数"}
基础合并: conf=soft_linear | unit_norm=domain_aware(不可省) | conflict=conservative_min 压力覆盖: near_infeasible→slack_buffer | adversarial→confidence_floor(0.6)
失败处理 [UX-5/6, TOK-14]
{"status":"FAILED","error_code":"INFEASIBLE|BAD_PARAMS|AMBIGUOUS|SOLVER_FAIL|OUT_OF_SCOPE",
"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。[UX-6] 反事实分析（用户请求时）。[UX-7]
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 | ❌ 多模糊点串行澄清 | ❌ 增量修改全量重解析 ❌ JSON含默认值 | ❌ 不活跃约束默认展开 | ❌ 失败后输出散文 ❌ 混合问题不触发COOP | ❌ COOP合并跳过domain_aware ❌ 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] ❌ FIX-19: 退化场景不加正则化 ❌ FIX-21: non_convex+adv使用均匀随机起点或thresh>0.020 ❌ FIX-22: non_convex+adv跳过双层防护（B层或A层缺一不可） ❌ FIX-23: mixed_bayes压力场景跳过专用策略