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 hajibabaie/combinatorial-optimization-skills --skill linearization-techniquesgit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-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/hajibabaie/combinatorial-optimization-skills/linearization-techniques)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/linearization-techniques"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/linearization-techniques/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/hajibabaie/combinatorial-optimization-skills/linearization-techniques"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/linearization-techniques.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 | $0.00128 | $0.13250 |
| Opus 5.5 | $0.00051 | $0.05300 |
| Sonnet 5.5 | $0.00026 | $0.02650 |
| Haiku 4.5 | $0.00013 | $0.01325 |
Grade A, and why
linearization-techniques 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 1mo ago.
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 — 859 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Linearization Techniques
You are an expert in reformulating nonlinear and logical model constructs as mixed-integer linear programs. This skill covers exact linearization of variable products, absolute values, min/max terms, piecewise-linear functions, logical implications, and fractional objectives, plus the discipline of choosing tight big-M constants. Use the framework below to classify each nonlinear term, pick the sharpest valid reformulation, and verify the result.
Initial Assessment
Establish these facts before proposing any reformulation:
- Inventory the nonlinear terms. List every product, absolute value, min/max, ratio, piecewise function, and if-then condition. The right technique differs per term type.
- Variable domains in each product. Binary times binary and binary times continuous have exact linearizations. Continuous times continuous does not — only relaxations (McCormick) or piecewise approximations. Confirm which case you are in before promising exactness.
- Finite bounds. Almost every technique here needs finite lower/upper bounds on the continuous variables involved. Ask where bounds come from: physical limits, capacity data, or bound-propagation. If a variable is genuinely unbounded, fix that first.
- Convex use or nonconvex use. A term like |w| or max(w1, w2) needs no binaries when the optimization direction already pushes it the right way (epigraph use). It needs binaries when used in the opposite direction. Identify the direction before adding integer variables.
- Where the term sits. Objective-only nonlinearity sometimes allows lighter treatment (epigraph, Dinkelbach) than nonlinearity inside constraints.
- Solver and license. Gurobi, CPLEX, and SCIP accept indicator constraints, SOS sets, and
native PWL/general constraints; a pure-LP or open-source pipeline may force manual big-M.
Gurobi can also solve bilinear models directly with
Params.NonConvex = 2— sometimes the honest answer is "do not hand-linearize." - Problem size after reformulation. Linearizing all products in a quadratic model with n² binaries creates O(n⁴) variables. Estimate the blow-up; pick a compact scheme (e.g. Kaufman–Broeckx) if the full one will not fit in memory.
- Accuracy requirement. Piecewise-linear approximation of a smooth function trades breakpoint count against error. Get a tolerance before choosing the grid.
- Numerical scale. Note the ratio between the largest and smallest constraint coefficients you are about to create. Big-M values that push this ratio past ~1e6 will cause solver trouble; plan bound tightening up front.
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.
- 1mo ago First seen · 859 lines · 128 tokens per session scan A 55194e7d4431
linearization-techniques is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (14 stars, last pushed 4mo ago), licensed MIT. It adds 128 tokens to every session and 13,250 once invoked, about $0.0005 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 2026-08-31.
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