The most fundamental optimization algorithm

The simplex method was the first algorithm invented that can solve large-scale linear programs. The inventor, George Dantzig, was arguably a genius, but the algorithm itself is simple enough that I can explain the main ideas in this video.

Optimal solutions for linear programs, if they exist, occur at vertices of the feasible region. We first spend some time getting an algebraic characterization of vertices.

Afterwards, we introduce a way to transform linear programs into “standard form,” after which the characterization of vertices becomes simpler.

Finally, we show how to perform iterations of simplex and what that means graphically. Simplex, at the end of the day, is just rewriting equations over and over.


Chapters:
0:00 Intro
1:30 Outline of Video
2:15 Characterization of Vertices
4:33 Putting an LP into Standard Form
7:20 Getting an Initial Vertex
9:40 Constructing the Simplex Tableau
11:00 Performing Simplex Iterations

References:

Journal excerpt from Computing in Science & Engineering:
https://www.cs.fsu.edu/~lacher/course...

Article on Two-Phase Simplex Method:
https://webspace.maths.qmul.ac.uk/fel...


Music:

Mesmerize by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/...

Source: http://incompetech.com/music/royalty-...

Artist: http://incompetech.com/