Optimization: Linear optimization

Introduction to linear optimization, duality and the simplex algorithm.

Description

Introduction to linear optimization, duality and the simplex algorithm.

What you will learn

• Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem.


• Constraints: you will learn how to represent the constraints of a linear optimization problem, both from a geometric and algebraic point of views.


• Duality: you will learn how to derive a companion problem called the "dual".


• Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution.


• Simplex method: you will learn an algorithm to solve a linear optimization problem.

Prerequisites

The course assumes no prior knowledge of optimization. It relies heavily on linear algebra, analysis and calculus (matrices, derivatives, eigenvalues, etc.)
The knowledge of the programming language Python is an asset to learn the details of the algorithms. However, it is possible to follow the course without programming at all.

Plan

The course is structured into 5 sections. 

• Formulation: you will learn from simple examples how to formulate, transform and characterize  an optimization problem.  


• Constraints: you will learn how to represent the constraints of a linear optimization problem, both from a geometric and algebraic point of views.


• Duality: you will learn how to derive a companion problem called the "dual". 


• Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution. 


• Simplex method: you will learn an algorithm to solve a linear optimization problem.