# Linear Programming Basics

Learn the simplex method, duality and sensitivity analysis for linear programs

Updated on Sep, 2023

Language - English

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## Course Description

Linear programming is a widely used optimization tool in various application (data science, engineering, transportation, supply chain, etc.). Linear programming also makes the basic  foundation behind complex optimization tools like Mixed Integer Liner Programming (MILP) and Column generation. In this course, we will study the basic theoretical concepts related to linear programming.

The course is organized as follows. In the first section, we will introduce linear programming, and we will explore the convexity and types of optimalities. Then, in the second section, we will build up on the basics to learn ways to solve the linear program using simplex method. We will then explore the concept of linear programming duality. We will also go through some of the hardest to understand concepts like strong duality, complementary slackness and Farkas' lemma. Furthermore, we try to understand these concepts in an easy-to-follow way. This allows one to obtain lower bounds on the minimization problem and provide a proof of optimality or Infeasibility. In the last section, we will explore how to perform sensitivity analysis (the effects of changing parts of a linear program). At the end of each section, there are assignments to help you evaluate your knowledge.

As you would have noticed, this course doesn't explore modeling optimization problems as a linear program much. That is a separate topic and deserves an entire course on it.

### Goals

What will you learn in this course:

• Describe what a linear program is.
• Solve a linear program using graphical and simplex methods.
• Compute the dual of the given linear program.
• Use the primal and dual values to prove optimality or infeasibility of the given linear program..
• Compute how the solution value changes under minor modification of the given linear program.

### Prerequisites

What are the prerequisites for this course?

• Basic knowledge of linear algebra is required to understand various proofs presented.
• No programming experience needed.

## Curriculum

Check out the detailed breakdown of what’s inside the course

Introduction
7 Lectures
• Introduction 03:07 03:07
• Example of a linear program 03:09 03:09
• Standard format and matrix representation 07:01 07:01
• Types of optimalities 01:36 01:36
• Existance of optimal solution 05:38 05:38
• Convexity 06:47 06:47
• Assignment 1
Solving linear programs
8 Lectures
Linear programming duality
9 Lectures
Sensitivity Analysis
6 Lectures
Conclusion
1 Lectures

## Instructor Details

Krunal Patel

I graduated from BITS Pilani Goa Campus in 2015 with B.E. (Hons.) Computer Science and M.Sc. (Hons.) Mathematics. After graduation, I worked with Google from 2015 to 2020 with operations research team. With the operations research team, I worked as a developer of Google OR-Tools. I Left Google in 2020 to start my PhD under the supervision of Prof. Andrea Lodi and Prof. Guy Desaulniers in applied mathematics.

My research interests:

Discrete optimization

Column Generation

Machine Learning.

## Course Certificate

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