V0.8.0
Agent Skill for constrained optimization via ALM/ADMM/KKT — with adversarial guards, COOP cross-skill protocol, and 20k-sim validated parameters
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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.
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SKILL.md
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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)
- 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]