Linear functions, polyhedra and linear programming problems

Part 1 of the course, volume 1 of the lecture notes. Linear functions (gradient, Hessian and level sets), half-spaces and polyhedra, linear optimization problems with their optimal solutions, examples and properties, the canonical and standard forms with the graphical method, possible outcomes and equivalences between forms.

Lecture notes, volume 1 (PDF)

• 1. Linear functions

  ---

  Linear functions

  Read the chapter

• 2. Half-spaces and polyhedra

  ---

  Half-spaces and supporting hyperplanes · Polyhedra

  Read the chapter · Exercises

• 3. Linear optimization problems

  ---

  Linear Programming problems · Examples and properties of linear optimization problems

  Read the chapter · Exercises

• 4. Linear Programming problems

  ---

  Canonical maximization form · Standard maximization form

  Read the chapter · Exercises

• 5. Possible outcomes and equivalent formulations

  ---

  The two reference forms · Infeasible and unbounded LP problems · Equivalent reformulations

  Read the chapter · Exercises