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:

Article on Two-Phase Simplex Method:

Music:

[vidblogger]

Thank you for introducing me to the Simplex method! Earlier this year, I learned how to write programs on my graphing calculator. (nerdiest thing I’ve ever done, I know) You inspired me to try to write a program to perform Simplex on my Casio. I just got it working today! It’s clocking in at the biggest, most complicated program I’ve written on the the calculator so far, but it works and I am a happy nerd. :D

[deez_gainz]

Great videos, would it be a good idea to show how simplex tableau is implemented on a computer? Because those increase decrease manipulations seem a bit arbitrary

[Sejiko]

dont get what this method archives... how would i apply it to a real world solution?

[tomoki-vo]

Great video.
why is it called simplex?

[xy]

You should have mentioned that if n-m is not equal to 0 then there is no bounded region=convex area= feasible area.