lp-duality

Derive dual linear programs from LaTeX or markdown inputs using a 7-step procedure.

Updated Jan 2, 2026
One-click install
npx skills add https://github.com/slahaie/lp-duality-skill --skill lp-duality
Or copy as Structured Prompt for Agent
Please help me install this Agent Skill.
Skill: lp-duality
Source: https://github.com/slahaie/lp-duality-skill/tree/main/.claude/skills/lp-duality
Command: npx skills add https://github.com/slahaie/lp-duality-skill --skill lp-duality

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

This Skill provides a structured, step-by-step method to transform a primal linear program (LP) into its dual form, ensuring clarity and correctness in the process.

Core Features & Use Cases

  • Systematic Dual Derivation: Follows a 7-step procedure to convert any LP into its dual.
  • Interpretability Preservation: Ensures that each step maintains the logical connection between the primal and dual problems.
  • Use Case: When a user provides a linear program in LaTeX or markdown and requests its dual form, or asks about the relationships and conditions of LP duality.

Quick Start

Use the lp-duality skill to find the dual of the following primal linear program: [User provides primal LP here].

Frequently Asked Questions about lp-duality

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I derive the dual of a linear program?

Linear programming duality transforms a primal LP into its dual counterpart using a systematic 7-step derivation procedure. The Skill accepts primal LPs in LaTeX or markdown format and outputs the transformed dual problem.

How do I derive complementary slackness conditions for a linear program?

To derive complementary slackness conditions, input your primal linear program in LaTeX or markdown format. The Skill systematically calculates the conditions and verifies primal-dual relationships during the transformation process.

What is the best way to convert a primal LP to its dual form step by step?

Converting a primal LP to its dual form step by step requires a systematic 7-step procedure. This approach transforms the linear program while preserving interpretability and maintaining the logical connection between the primal and dual problems.

Can I use LaTeX format to input linear programming problems for dual conversion?

Yes, you can input linear programming problems using LaTeX format for dual conversion. The Skill specifically handles LPs provided in LaTeX or markdown format, transforming them into their dual counterparts while preserving interpretability.

How does mathematical modeling handle primal-dual relationships in operations research?

Mathematical modeling handles primal-dual relationships in operations research by systematically transforming primal linear programs into their dual counterparts. This Skill verifies primal-dual relationships and ensures interpretability throughout the 7-step derivation process.

Why does my manually derived LP dual not match the primal problem interpretation?

A manually derived LP dual may not match the primal problem interpretation if the transformation lacks a systematic procedure. Using a structured 7-step derivation ensures each step maintains the logical connection between the primal and dual problems.