Formulate, analyze, and certify linear programming models with duality proofs.
npx skills add https://github.com/Arcadi4/nerdy --skill linear-programming-arcadi4
Please help me install this Agent Skill. Skill: linear-programming Source: https://github.com/Arcadi4/nerdy/tree/main/clrs/linear-programming Command: npx skills add https://github.com/Arcadi4/nerdy --skill linear-programming-arcadi4
This skill provides a rigorous framework for formulating, solving, proving, and auditing linear-programming models, ensuring that each decision variable has a real interpretation and that optimality can be certified through duality or complementary slackness.
Create a formal LP model for a resource allocation problem and verify feasibility and optimality.
High-intent search queries and answers about installing and using this skill.
Linear programming optimality is certified by constructing the dual problem and verifying complementary slackness conditions. This framework checks that every decision variable and constraint satisfies strict slackness, providing mathematical proof of primal-dual feasibility and boundedness.
A Farkas certificate provides mathematical proof of linear programming infeasibility. It is needed when standard solvers return infeasible models, using Farkas' lemma to certify that no feasible solution exists for the given constraint set.
Converting linear programming models to standard form involves transforming inequality constraints into equalities using slack variables and ensuring variables are non-negative. This workflow applies directly to resource allocation, scheduling, and network-flow problem formulations.
Integer-LP caveats include integrality gaps and the loss of strong duality guarantees. When modeling network-flow or scheduling problems, decision variables requiring integer values prevent direct application of standard complementary slackness proofs.
Yes, the linear programming workflow explicitly handles unboundedness checks and feasibility analysis. It applies dynamic rules for certificates to reason about boundedness and verify whether constraint sets admit feasible solutions across resource allocation and network-flow formulations.
NVIDIATranslate natural-language problem statements into explicit LP/MILP formulations.
slahaieDerive dual linear programs from LaTeX or markdown inputs using a 7-step procedure.
bnebNLP-based grammar and style correction for your writing, available as a VS Code extension and/or standalone Python library.
NVIDIABuild and solve LP, MILP, and QP models with NVIDIA cuOpt's Python API.
