[1005 OFF] Linear Programming basics

 

Linear programming is an indispensable optimization tool that finds applications across diverse fields, from data science and engineering to transportation and supply chain management. It serves as the fundamental building block for more complex optimization techniques like Mixed Integer Linear Programming (MILP) and Column Generation. In this course, we delve into the theoretical underpinnings of linear programming, equipping you with the knowledge and skills to harness its power effectively.

Course Overview

This course is structured to provide a deep understanding of linear programming. Here's an outline of what you can expect:

Section 1: Introduction to Linear Programming

We begin with an introduction to linear programming, exploring its foundational concepts and principles.

Delve into the world of convexity and various types of optimality criteria.

Section 2: Solving Linear Programs

Building on the basics, we dissect the simplex method, a powerful technique for solving linear programs.

Uncover the concept of linear programming duality and its practical implications.

Navigate through advanced topics such as strong duality, complementary slackness, and Farkas' lemma, making these often complex concepts approachable.

Section 3: Sensitivity Analysis

Learn how to perform sensitivity analysis, understanding how changes in the linear program's parameters affect the solution.

Gain insights into obtaining lower bounds, providing evidence of optimality or infeasibility.

Assignments

Throughout the course, you'll have the opportunity to apply your knowledge with carefully crafted assignments.

While this course primarily focuses on the theoretical aspects of linear programming, it doesn't delve deeply into the art of modeling optimization problems as linear programs. Modeling, a distinct topic, deserves its own dedicated course.

Prerequisites

Basic linear algebra knowledge is essential for comprehending the proofs and concepts covered in this course.

Get the Support You Need

If you encounter challenges during the lectures or assignments, don't hesitate to reach out for assistance. We're committed to helping you succeed.

Schedule office hours from our website, available on a first-come, first-served basis, to clarify any doubts or questions you may have.

Mastering linear programming is a valuable skill in today's data-driven world. This course empowers you to tackle optimization problems with confidence and precision. Start your journey toward optimization excellence today!