Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill optimization-and-operations-researchgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/optimization-and-operations-research)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/optimization-and-operations-research"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/optimization-and-operations-research/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/optimization-and-operations-research"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/optimization-and-operations-research.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00067 | $0.00575 |
| Opus 5.5 | $0.00027 | $0.00230 |
| Sonnet 5.5 | $0.00013 | $0.00115 |
| Haiku 4.5 | $0.00007 | $0.00057 |
Grade A, and why
optimization-and-operations-research scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 34 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Optimization & Operations Research
Formulation
Decision variables -> objective -> constraints; classify: LP, QP, convex, nonconvex, integer, stochastic.
Linear programming
- Standard form max c^T x s.t. Ax <= b, x >= 0; optimum at a vertex; simplex method; interior-point methods (polynomial time).
- Duality: min b^T y s.t. A^T y >= c; strong duality (equal optimal values); complementary slackness; shadow prices; sensitivity analysis.
- Special cases: transportation, assignment, shortest path, max flow as LPs.
Convex & nonlinear
- Convex set/function; local min = global min; first-order condition f(y) >= f(x) + grad f(x)^T (y - x).
- KKT conditions: stationarity, primal/dual feasibility, complementary slackness; Slater's condition gives strong duality.
- Algorithms: gradient descent (step 1/L, rate O(1/k), strongly convex linear rate), accelerated (Nesterov), Newton (quadratic local), quasi-Newton (BFGS), conjugate gradient, proximal methods, ADMM, SGD and Adam for ML, trust regions.
- Nonconvex: local minima, saddle points, random restarts, simulated annealing, genetic algorithms, Bayesian optimization.
Discrete & dynamic
- Integer programming: branch and bound, cutting planes, total unimodularity; knapsack, TSP, scheduling.
- Dynamic programming: Bellman principle, optimal substructure (knapsack, edit distance, shortest paths); Markov decision processes, value iteration, reinforcement learning basics.
- Calculus of variations: Euler-Lagrange equation d/dx(F_y') = F_y; brachistochrone, geodesics, isoperimetric problem; optimal control (Pontryagin).
- Game theory: Nash equilibrium (existence by Nash/Brouwer), zero-sum minimax (von Neumann), prisoner's dilemma, mixed strategies, auctions, mechanism design.
- Queueing, inventory (EOQ = sqrt(2DS/H)), scheduling.
Script
scripts/optim_tools.py has a simplex-free LP via scipy, gradient descent with line search, Newton, and knapsack DP examples.
Answer format
State model, solver or method, optimal value and solution, check feasibility and optimality (duality gap or gradient norm).
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 34 lines · 67 tokens per session scan A f5b6634f7bdc
optimization-and-operations-research is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 67 tokens to every session and 575 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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