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
More problems: slama.dev/youtube/linear-prog...
Made as my entry to SoME3: 3blue1brown.substack.com/p/so...
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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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Source code: github.com/xiaoxiae/videos/tr...
Music (in the order it appears in the video):
► Cases to Rest by Blue Dot Sessions: app.sessions.blue/browse/trac...
► Thannoid by Blue Dot Sessions: app.sessions.blue/browse/trac...
► ZigZag Heart by Blue Dot Sessions: app.sessions.blue/browse/trac...
► Maisie Dreamer by Blue Dot Sessions: app.sessions.blue/browse/trac...
► Night Light by Blue Dot Sessions: app.sessions.blue/browse/trac...
Software used:
► Manim (animation software): github.com/ManimCommunity/manim/
► Kdenlive (video cutting): kdenlive.org/en/
► ffmpeg (audio/video processing): ffmpeg.org/
► OBS (audio/video recording): obsproject.com/download
► arecord (audio recording): linux.die.net/man/1/arecord
► sox (audio processing): sox.sourceforge.net/
► Inkscape (vector image editing): inkscape.org/
► Midjourney (image generation): www.midjourney.com/app/
Social media:
► Website (for other things I'm up to): slama.dev/
► Patreon (if you'd like to support me): / ytoms
Thanks to Matěj Kripner, Martin Balko, Lucia Zhang, Václav Rozhoň (@polylog), Kateřina Sulková, Mohit Shrestha, Teo Tuicu and Tomáš Sláma (my dad, not me) for valuable feedback.
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[EN] Gerard Sierksma; Yori Zwols (2015). Linear and Integer Optimization: Theory and Practice
www.taylorfrancis.com/books/m...
[CZ] Přednáška Jiřího Sgalla: Lineární programování a kombinatorická optimalizace
iuuk.mff.cuni.cz/~sgall/vyuka...
[EN] George B. Dantzig (1982): Reminiscences about the origins of linear programming
apps.dtic.mil/sti/pdfs/ADA112...

[@johankotze42]

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.

[@IxCIHAoX]

@johankotze42 Interesting, i always wondered how an industrial engineer would apply Operations Research in pratice. We had to calculate the simplex by hand, but i always thought i would just use some excel plugin. I'll soon graduate in industrial engineering and am curious about key skills that you dont learn in uni. If you don't mind, what would you like to see more in upcoming IEs?

[@greatcanadianmoose3965]

@@IxCIHAoX I mean look up the excel solver... I've learnt both doing it by hand, as well as excel, though currently I'm learning GUSEK to solve these problems!

[@fabio.1]

👀

[@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 much!!!!!!!

[@payrimdwein9082]

just saw this after my course finished, this is good!

The way I always understood it is that most problems are either seen as you taking up resources to maximize a profit or you are minimizing your wasted money by emptying out your storage space. In the example, you are either making potatoes/carrots to get a profit or you are essentially trying to use as much seeds and fertilizers as possible to have the least waste.

[@jainickvishani5185]

EXACTLY, I just finished my finals last week and I see this video explaining the whole damn course 😂

[@spb1179]

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.

[@Alexander-oh8ry]

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

[@YTomS]

Thanks for the kind words and the comment (you're right, the definitions were incorrect), I updated the website.

[@ColinTimmins]

@@YTomSStating the fact that you had a correction to make and corrected it gets an extra sub from me. Thanks for the content. I’m now getting back into programming. 😊

[@socratesphilanthropy4937]

I have heard black hole . Rabbit hole? Thanks 4 the new term from an indian

[@markgreen2170]

@@socratesphilanthropy4937 and now we have a new one 'bonus hole'

[@Ocara31]

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

[@demr4921]

Damn right!

[@gigantopithecus8254]

what about nonconvex instaid

[@juanhbiancuzzo1490]

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.

[@teodorticu2628]

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!

[@protiumdev]

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

[@VictorUn1]

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 !

[@Noxafurry]

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

[@prathameshsundaram7509]

I love how thorough your videos are! Thanks a ton.

[@stjintje]

Wow, well explained! I struggled to get through my linear programming course for 2 years, but you make it seem so simple!

[@ShashankEarth]

Excellently explained!!! What a great visualization video. Waiting for more videos on Simplex and Dual Simplex. Thank you so much.

[@juan.araujonog]

I just found your channel and this is so good. You should really be proud of your work!

[@victormanuel8767]

This is brilliant. You really blended theory and practical application into one cohesive whole.

[@puneetkumarsingh1484]

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.

[@Erik_The_Viking]

Beautiful video! Well done with a simple example to show the concepts.

[@sarkaholendova9080]

Wow, what a quality! I am blown away. The best video yet! Thank you :)

[@timelygoose]

The best explanation on this topic that I've come across, thank you sir!

[@user-gc6bb1tk9h]

Phenomenal video. Very well explained. This is so helpful! Simple explanation, great work sir!.

[@ehsanabbasi6218]

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!

[@blllannnnk]

this is an absolutely amazing video. It's animations are so beautiful and illustrate the essence of the method. After watching the video, I can confidently say that I have some real understanding of linear programming! Thanks a lot!

[@beach_bum_dev]

Great video, instant sub. I look forward to more high quality videos such as this one

[@samuelkhzym9442]

Phenomenal video! We are going through the simplex method in my linear optimization class and it was very difficult to grasp the process, let alone the intuition behind it. Thank you for making it :)

[@user-vx6zk5jj4e]

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.

[@feeelix]

Awesome video! I believe it's only a matter of time until your channel takes off

[@neobrandsainclair3407]

I struggled with linear programming when I was a student, but you explained it so well that it's easier for me to understand how it works. Thank you :)

[@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!

[@lydianlights]

I used linear programming to solve for optimal production chains in the game Satisfactory! I made an online tool and everything. To be honest I just discovered that it was a well studied class of problems and downloaded a library to do it for me, haha. I knew vaguely there was "something, something simplex method" going on under the hood but I never truly studied the algorithm. Cool to see the geometry of how it actually works!

[@blackbriarmead1966]

satisfactorycalculator?

[@lydianlights]

@@blackbriarmead1966 I made "yet another factory planner". I would post the link but KZbin would probably eat it.

[@AlleBalle54]

great video, perfectly explained. Looking forward to the next one :)

[@DuongNguyen-dz8pb]

This is so helpful! Simple explanation, great work sir!

[@benwinstanleymusic]

Incredible video, thank you so much Tom! Helps so much with my optimisation course

[@pablocasas1001]

This video is simply wonderful please keep explaining linear programming(and hopefully any convex as well)

[@guitarljm]

We need your next video!! Amazing stuff.

[@namesurname1869]

As an industrial engineering student who is currently studying integer LP this video has to be the best way to get a grasp of the topic. Looking forward to you getting deeper into these concepts.

[@sanjaykrish8719]

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

[@arhamhundia3039]

Amazing video really helped me understand, thank you, please keep on making more videos.

[@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

[@TheLoopesMan]

Great work as usual boss

[@ajk7868]

You are amazing, I was hopping to find a mathematical channel like this

[@TrollFunMineMafia]

i remember doing this in university and not understanding a thing, now it all makes way more sense! thank you

[@tunafllsh]

Good job! This summarizes the course I took on LP.

[@jackninja1]

Absolutely excellent explanation!

[@adolfninh23]

detail and down-to-earth explanation

[@michaelangel7907]

Great! superb graphics, clear explanations. thanks

[@polares8187]

This video was amazing. Well created 💪💪

[@lucareale7161]

Phenomenal video. Very well explained

[@zoom8370]

Nice one! This put a smile on my face.

[@giovannihernandez3208]

This is amazing. I could understand what the dual is more intuitively.

[@ojcgv21]

this is an awesome video man, congrats!

[@gabedarrett1301]

Finally, an intuitive explanation of the simplex method! Your content matches that of 3blue1brown in terms of quality and ease of understanding! Subscribed Also, you might want to number the x1 and x2 tick marks

[@aglotgaming4660]

what nice video

[@felipenoleto166]

bro I'd pay to watch the continuation, very well explained!

[@pedrocolangelo5844]

Seriously, I have not been this excited with a KZbin 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.

[@macroxela]

Check out Reducible, similar to 3blue1brown but about computer science topics. He's just as good.

[@azfarahsan]

WHERE WAS THIS VIDEO WHEN I WAS STUDYING LINEAR PROGRAMMING GOOD VIDEO CONGRATS 👏🏼👏🏼

[@andrewcpu]

Wow, just found your channel. Love it.

[@adamdemeter6963]

Quality work! Well done.

[@alejrandom6592]

Wow this made me realize linear programming is a lot less boring than what school makes it look like. Great video ♡

[@dylanrandle]

Great video, thank you! Please keep it up!

[@Adityarm.08]

This was done so well! Thank you.

[@darshagarwal8307]

amazing stuff, I am working on recommender systems, and this has been quite helpful! You have just gained a subscriber :)))

[@Efesus67]

Wow, this is awesome. The knapsack problem almost feels like it could be posed in discreet probability theory: given a random variable X, find a finite subset A of X that will maximize E[A] (=sum of p_i•x_i) and the sum of the chosen values x_i do not exceed a number k. Thanks for your website!

[@frannaglic4628]

Great video! Good work sir.

[@albertn0855]

This videos is inspiring to me as I'm considering operations research as my main field of study as an applied mathematician!

[@innokentiyromanchenko1450]

thanks for your videos, they are excellent

[@porschepanamera92]

Very nice intro to LP. I've read about slack variables, and now they make more sense. I would love to see a follow-up to N variables, which makes it less intuitive without the geometric interpretation, and a brief note on convexity. Nonconvex optimization problems require some more exotic methods :)

[@bugs-hl5jf]

Really amazing explanation. Thank you.

[@user-hy6cp6xp9f]

I love this, thanks so much for sharing

[@TheTaekwondo1996]

Thanks a lot, the video was really helpful and the explanation was very clear

[@priyanshugoel3030]

Okay that explained slack,surplus and basic variables pretty well.

[@dilu4202]

vivid video！love it！

[@pierre2693]

Excellent video!

[@ridazouga4144]

Maaan thaaaanks for sharing this amazing content👏👏👏👏

[@nhaho1473]

Thank you for this video, it's very useful for me .

[@ishungchan]

Thank you, I'm struggling with this course at my uni. Your video helps me understand it 🙏

Thank-you for this! Or should I say - děkuju? Finally someone from my country using manim and creating videos that I really enjoy watching! Keep up the great work - you have a sub from me :) Měj se!

[@FaffyWaffles]

I love this use of Manim. So High Quality! New Subscriber is me.

[@jackgude3969]

I really like the background music. Very cosy math video.

[@mohitduggal007]

Great explanation 👍

[@StentorCoeruleus]

This is probably the most useful thing I’ve ever learned of since learning to breathe

[@ivanperica3731]

My college professor was not bad, but this video is something else. Really utilising the technology to present complex topics in such an amazing way. I am aware of how complex and immensly time consuming these types of videos get, but please do continue making these.

[@corlaez]

I found the answer intuitively as soon as the problem was presented (which is super simple of course) but it was interesting to see (around the 9:22 mark) that my logic to arrive to that answer is exactly the Dantzig's pivot rule. Thanks for the video it is super interesting that this intuition of mine has been reinforced by this method and that it can apply to more complex inequalities and more dimensions!

[@jorgemelendez6536]

This is a great lecture. Thanks

[@WavyB1]

i was waiting anxtiously. for the Brilliant AD. And was pleased that the video was just pure knowledge. Thank you. For this, here is a LIKE and SUBSCRIBE!!!

[@alexanderkurz2409]

beautiful video ... thanks

[@miriamramstudio3982]

Great video. Thanks

[@samarthtandale9121]

Love this video , really ❣️💯❣️

[@electra_]

I hope you make more videos on this subject! We mentioned linear programming in school, but not much more other than "yeah you can plug in numbers to this library and it works" which was quite dissapointing... i want to know how and why it works.

[@fawwazanvilen6625]

omg you showing duality was mindblowing

[@hazel_moonshine]

Very well made video 👍

[@tatolela1234]

I dont usually writte comments, but in this time i had to. sincerely spectacular explanation.

[@kofiboamah8242]

i got confused from 5:45 the loosening and tightening, simplex method... i even got more confused with the introduction of the slack variables... I have saved this video i hope to watch it several times till i get it. Thank you very much for a great video

[@tahirhanif9669]

Excellent, thank you

[@SorokinAU]

very intrestin! thank you very much!

[@JRoadzReegz]

Thank you this is amazing!!!!!

[@princewaesen154]

you bothered to explain the concept of duality which my university prof just didn't feel like doing. Thank you

[@debasiskar4662]

Waiting for many more videos of similar type.

[@newtral6303]

Please bring out more videos and continuation of this series on LP, ILP & MILP.

[@Sebastian-wx2td]

Amazing video