The Art of Linear Programming

A visual-heavy introduction to Linear Programming including basic definitions, solution via the Simplex method, the principle of duality and Integer Linear Programming. #some3

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Timetable:
0:00 - Introduction
0:26 - Basics
3:44 - Simplex Method
11:47 - Duality
14:01 - Integer Linear Programming
17:31 - Conclusion

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Music (in the order it appears in the video):

Software used:

Social media:

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[EN] Gerard Sierksma; Yori Zwols (2015). Linear and Integer Optimization: Theory and Practice

[CZ] Přednáška Jiřího Sgalla: Lineární programování a kombinatorická optimalizace

[EN] George B. Dantzig (1982): Reminiscences about the origins of linear programming

[johankotze]

This is so interesting. I am retired now, but the last 20 years of of my working life was spent managing a dynamic truck allocation system in an opencast mine. I was mostly involved in the IT/IM side, but I knew the optimization was done with the simplex algorithm. Over the years, however, I got the impression that all the graduated industrial engineers did not understand what they were working with.I'll rewatch all of this a number of times.

[mathfincoding]

I took multiple operations research classes in undergrad and I'm taking math graduate classes now. I never truly understood the connection between the primal and the dual problem until now. My mind is blown. Thank you so

[spb]

This topic has to be one of the most important things I’ve seen this year. So useful. That’s crazy what you could do with this.

[bejoscha]

Perfect pace, well thought of outline, clean and helpful visuals, good narration - what is not to love about this? You've gained a subscriber.

[Ocara]

Please, make about Non Linear Programming and also about Combinatorial Optimization. Your work is really fantastic!

[Alexander-ohry]

Im impressed by your website and ran hours deep into a mathematical rabbit hole on Wikipedia. Thanks, I unexpectedly learned a lot today! But i noticed that on your website, the description of the maximum independent set problem and minimum vertex cover problem are wrong and mashed together

[puneetkumarsingh]

Took me 2 watches on separate days while thinking about it in between to fully understand the slack loosening and tightening concept. And when it clicked, it felt really beautiful and made sense! Thanks for making it so clear.

[xcoder]

The initial problem looks way too simple ... because it is. Of course you plant as many carrots as you can and fill the rest with potatoes. Probleme solved. To make the initial problem more complex, just add in two other factors: The amount of farmland is also limited and potatoes provide way more yield per square meter than carrots do. Yet carrots grow faster and you could sow and harvest carrots twice a season but potatoes only once. And there you have a problem you cannot solve in your head any longer, yet that is a real world problem a farmer might face.

[juanhbiancuzzo]

this is my first video of you that I've seen, and it's really amazing. i'm looking forward to seeing more videos in this series.

[protiumx]

Thank you for all the work you put in these videos, I really learn a lot with them!

[teodorticu]

I love your videos! It feels like you explain complex things in a way that really makes them easy to understand. Your content always triggers my interest and I find myself going into rabbit holes online lol. Keep it up!

[iFastee]

cool... it would be nice to mention that most hard problems are non-linear, non-convex, can be part of the branch of discrete decisions where it becomes computationally unscalable to use certain linear algorithms, can be multimodal (or multiobjective)... and that's where heuristic and stochastic algorithms (that have a lot of generalizations of the linear programming field) enter to even try to tackle them

[ehsanabbasi]

Truly impressed by this video! As an industrial engineer, it was a challenge to learn and visualize the concept of LP and SIMPLEX. What I learned in 19 minutes from this video is comparable to my 4-month university course. Now I wish you had created this video 3 years ago. Thanks!

[OgsLike]

Wanted to say that besides your excellent knowledge on the subject, it’s an extremely rare and precious talent you have of teaching and presenting complex subjects in an accessible way. Your visuals, audio, pace and use of humour is exceptional. You have a multi-million dollar talent that I hope you benefit from!

[sanjaykrish]

Your work will impact generations to come and uplift the knowledge of people who are at a disadvantage. Thanks a lot

[VictorUn]

I've just discovered your channel and when I finished the video I thought you would have more subscribers. The quality is mind-blowing, keep going !

[ycmrtgz]

that was really fun to watch. Thanks man I haven't took a math class in a while but, I was decently good at understanding math. You have a great way of explaining things and I love it! Keep up the content made me realize how much I loved math when I was taking it back then!

[vxzkjje]

I appreciate that you are giving the real meaning behind each step instead of just throwing some random numbers and math operations like most other creators do.

[pedrocolangelo]

Seriously, I have not been this excited with a YouTube channel since I discovered 3blue1brown, and that must be about 3 years ago.

Sir, what a masterpiece it is. Thanks for sharing it with us.

[Noxafurry]

This is some 3Blue1Brown quality level of quality! I am genuinely shocked by how good this video and the explanation is! Thank you.