What Is Mathematical Optimization?

Ғылым және технология

A gentle and visual introduction to the topic of Convex Optimization. (1/3)
This video is the first of a series of three. The plan is as follows:
Part 1: What is (Mathematical) Optimization? ( • What Is Mathematical O... )
Part 2: Convexity and the Principle of (Lagrangian) Duality ( • Convexity and The Prin... )
Part 3: Algorithms for Convex Optimization (Interior Point Methods). ( • The Karush-Kuhn-Tucker... )
-------------------------------
Typos:
- 8:34, The matrix A should be of size nxm, and the vector b should be of size 1xm.
--------------------------------
Timestamps:
0:00 Intro
2:50 What is optimization?
06:00 Linear programs
8:19 Linear regression
9:32 (Markovitz) Portfolio optimization
10:00 Conclusion
--------------------------
Credit:
🐍 Manim and Python : github.com/3b1b/manim
🐵 Blender3D: www.blender.org/
🗒️ Emacs: www.gnu.org/software/emacs/
This video would not have been possible without the help of Gökçe Dayanıklı.
--------------------------
Music
Sneaky Snitch by Kevin MacLeod
Link: incompetech.filmmusic.io/song...
License: filmmusic.io/standard-license
Carefree by Kevin MacLeod
Link: incompetech.filmmusic.io/song...
License: filmmusic.io/standard-license
Funkorama by Kevin MacLeod
Link: incompetech.filmmusic.io/song...
License: filmmusic.io/standard-license

Пікірлер: 94

  • @mirandac1364
    @mirandac136411 күн бұрын

    This is such a great video on so many levels. May god bless the people who had a hand in making it 🙏🏻🙏🏻

  • @SandeepSinghPlus
    @SandeepSinghPlus Жыл бұрын

    After Stanford's Stephen Boyd's original lecture, this is most well explained content of Convexity Optimization, Thanks for doing beautiful work!

  • @arisioz

    @arisioz

    Жыл бұрын

    Check out Constantine Caramanis too, he has such a firm grasp of the topic and he's really got those teaching skills

  • @sando_7
    @sando_72 жыл бұрын

    This is what I was always looking for! I appreciate your hard work :)

  • @wenzhouli7104
    @wenzhouli71042 жыл бұрын

    Thank you so much for the video! This is a small but high-quality channel!

  • @fumseck
    @fumseck2 жыл бұрын

    This series is absolutely formidable. thank you!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Glad to hear it!

  • @lopyus
    @lopyus2 жыл бұрын

    Wow I took this course last year, you covered a lot of material in such a short time. It is amazing, I hope all of the courses could be made in form of such high quality videos someday. Great work 👍👍

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Great to hear, thanks!

  • @cutestbear3327
    @cutestbear3327 Жыл бұрын

    I took a class that I am not ready for and your videos have absolutely rescued me 😂

  • @VisuallyExplained

    @VisuallyExplained

    Жыл бұрын

    Good to hear :D

  • @_soundwave_
    @_soundwave_8 ай бұрын

    Underrated. As is most channels of maths andscience.

  • @ThamizhanDaa1
    @ThamizhanDaa12 жыл бұрын

    highly highlu underrated channel and videos

  • @vtrandal
    @vtrandal Жыл бұрын

    Bravo my friend, you are a star. This content is superb!

  • @sanchayanbhowal4446
    @sanchayanbhowal44463 жыл бұрын

    Really nice videoss. Continue to amaze us. ❤️

  • @priovag2632
    @priovag2632 Жыл бұрын

    Great work, honestly. Thank you very much.

  • @qusayhamad7243
    @qusayhamad7243 Жыл бұрын

    Thank you very much for this amazing and simple explanation

  • @joaquinacevedo9332
    @joaquinacevedo93322 жыл бұрын

    What a great video! Thanks!

  • @hexalgo5506
    @hexalgo55062 жыл бұрын

    clean, suave and very informative content

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thanks Mr Majdoub, appreciate it ;)

  • @user-ws8jm8uq4c
    @user-ws8jm8uq4c Жыл бұрын

    an amazing vid to understand the background from a scratch!

  • @josecarlosferreira4942
    @josecarlosferreira49423 жыл бұрын

    Nice work!

  • @trerortreror6636
    @trerortreror66363 жыл бұрын

    This is amaizing !!!

  • @darkside3ng
    @darkside3ng Жыл бұрын

    Amazing explanation!!!!

  • @EW-mb1ih
    @EW-mb1ih2 жыл бұрын

    your video is amazing! you are a gift for learning people!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thank you so much!

  • @brahimerraji9332
    @brahimerraji93322 жыл бұрын

    Im a newbie to convex opt and this video sure made things less shaky in my brains.I have a feeling in my gut telling me you are a fellow Moroccan. if so, bghit ghir ngol tbarklah 3lik et bonne continuation.

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Wonderful! It's great to meet a fellow moroccan in the wild ;)

  • @sukanya4498
    @sukanya4498 Жыл бұрын

    Love the animation ! ❤

  • @AJ-et3vf
    @AJ-et3vf Жыл бұрын

    awesome video. Thank you!

  • @moustafarahal3396
    @moustafarahal33962 жыл бұрын

    deserves big applause!! very informative in the smoothest way possible. Keep it up. But would be great if you work on audio quality as well.

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thank you, I appreciate that! I am working on improving audio. How does it sound to you? Is it noisy? "echo-y"? or is it just that the overall quality is not great?

  • @moustafarahal3396

    @moustafarahal3396

    2 жыл бұрын

    @@VisuallyExplained I'd say both noisy and echo-y. you can notice that especially when there is an "S" sound. waiting for more vids ;)

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    @@moustafarahal3396 that makes sense, thanks for the feedback!

  • @lebronx9516
    @lebronx95162 жыл бұрын

    Great explanation and animation! I wish you could do more optimization videos!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    More is coming very soon, stay tuned!

  • @nu11y61
    @nu11y612 жыл бұрын

    got here from a reddit post :) this is so cool man!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Awesome, thank you!

  • @cpimim
    @cpimim2 жыл бұрын

    Très beau travail

  • @hjx1981
    @hjx1981 Жыл бұрын

    excellent!!

  • @zhess4096
    @zhess40962 жыл бұрын

    Helped a lot in econ class thanks

  • @montagne13
    @montagne137 ай бұрын

    شكرا سي البشير أستعمل فيديوهاتك في دروسي و أشجع الطلبة على متابعتها تحية من المدرسة الوطنية للعلوم التطبيقية في طنجة طارق الزجاري الادريسي

  • @VisuallyExplained

    @VisuallyExplained

    7 ай бұрын

    شكرا جزيلا استاذي العزيز !

  • @sarahebal4391
    @sarahebal43917 ай бұрын

    Thank you very much for this amazing and simple explanation, can you do another one about non-convex optimization?

  • @KhanhNguyen-cx9uu
    @KhanhNguyen-cx9uu2 жыл бұрын

    Nice explanation

  • @Zyphoara
    @Zyphoara10 ай бұрын

    Life saver😭❤️

  • @brainxyz
    @brainxyz2 жыл бұрын

    Very nice, well done

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thank you! Cheers!

  • @mohamedel-kholy1436
    @mohamedel-kholy14362 жыл бұрын

    great effort thanks

  • @giovania.valdrighi1562
    @giovania.valdrighi15622 жыл бұрын

    I sent this video for all my friends

  • @ssrini2002
    @ssrini200210 ай бұрын

    4:40 here's a suggestion for visualizing 4D that i came up with. Use colour scales in a 3D space. The global maximum is a specific shade of green, the global minimum is a specific shade of red and all other points are an interpolation of these colours. It's not perfect and it definitely wouldn't work well for unbounded functions but it's still useful nonetheless.

  • @montagne13

    @montagne13

    7 ай бұрын

    Hi do you have a working example in python or mathematica .. thanks

  • @brysonpage4185
    @brysonpage4185 Жыл бұрын

    Thank you!

  • @MZmakesgames
    @MZmakesgames2 жыл бұрын

    Great series! Could you tell me what tool you use for neat animations like this?

  • @MZmakesgames

    @MZmakesgames

    2 жыл бұрын

    I just checked the description, and i think the answer is blender. Thanks for the great work!

  • @thebifrostbridge3900
    @thebifrostbridge39002 жыл бұрын

    Really nicely done. Sorry to come off as complicated, but could I persuade you to reupload your videos without the music in the background. I feel it is super distracting.

  • @mutalasuragemohammed6954
    @mutalasuragemohammed69542 жыл бұрын

    wonderful presentation

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thanks a lot!!

  • @Speak4Yourself2
    @Speak4Yourself2 Жыл бұрын

    Thanks a lot!

  • @yourweebtv8733
    @yourweebtv87339 ай бұрын

    THANKS

  • @azmyin
    @azmyin2 жыл бұрын

    Awesome lecture. What software did you use to create these animations?

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thanks!! I put some links in the video description

  • @salmaabdelmonem7482
    @salmaabdelmonem74822 жыл бұрын

    cool explanation😁

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thanks! 😃

  • @davidbellamy1388
    @davidbellamy13882 жыл бұрын

    Love your content so much. Btw, the NYT article was from 1984 not 1987!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Yes! Thank you! I will add a note in the video description

  • @jajhall
    @jajhall2 жыл бұрын

    Excellent material - I've seen a few so far. Only thing I'd quibble with is that your linear regression example has a square matrix A so (obviously) it's only an optimization problem if the rank is deficient. I'm an expert in solving linear programming problems BTW

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thank you for watching so attentively! Nice catch, b should be of size 1xm, and A should be of size nxm.

  • @jajhall

    @jajhall

    2 жыл бұрын

    @@VisuallyExplained And (obviously) the matrix itself should be "portrait" profile to stress the overdetermined nature of the equations. If you give the simplex method a hard time Vs interior point, I might be back with more comments 🙂

  • @shahidulislamzahid
    @shahidulislamzahid4 ай бұрын

    thanks

  • @niteshkumar0202
    @niteshkumar0202 Жыл бұрын

    WHAT TOOL DO YOU USE TO MAKE SUCH KIND OF VISUAL VIDEOS

  • @zyansheep
    @zyansheep2 жыл бұрын

    The intro is way too long, but the blender animations are so satisfying!

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    Thanks for the feedback?

  • @nadeemsharif8954
    @nadeemsharif89542 жыл бұрын

    Great.

  • @farshidshateri2833
    @farshidshateri28332 жыл бұрын

    That "Pi" reminded me of 3Blue1Brown!

  • @linyidai9076

    @linyidai9076

    2 ай бұрын

    its open source now. the tool 3b1b used. kudos to 3b1b!

  • @yangyu3122
    @yangyu3122 Жыл бұрын

    What software did you use to create the examples?

  • @VisuallyExplained

    @VisuallyExplained

    Жыл бұрын

    Manim, blender3d, and adobe premiere

  • @nurzaur
    @nurzaur2 жыл бұрын

    Do i understand you right: feasible set is the set of those x that we can pick considering our constraints, feasible region is the set of all f(x) that we can get ?

  • @VisuallyExplained

    @VisuallyExplained

    2 жыл бұрын

    I should have made it more explicit, but for me “feasible region” is the same thing as “feasible set”, which is the set of the “x”s that we are allowed to pick. Great question!

  • @nurzaur

    @nurzaur

    2 жыл бұрын

    @@VisuallyExplained thanks!

  • @SchoolofAI
    @SchoolofAI11 ай бұрын

    "General audience" requirements: linear algebra and calculus

  • @Sandstorm-ee4ef
    @Sandstorm-ee4ef8 ай бұрын

    Really a great video and I appreciate it a lot, could you also remove the background music, the video will be better so much without it.

  • @VisuallyExplained

    @VisuallyExplained

    8 ай бұрын

    Thank you! Appreciate your feedback

  • @handing2857
    @handing28576 ай бұрын

    Amazing! saved my ass

  • @gelamegeneishvili7240
    @gelamegeneishvili7240 Жыл бұрын

    God bless your bloodline

  • @gelamegeneishvili7240

    @gelamegeneishvili7240

    Жыл бұрын

    Generational blessing my man, you helped ton

  • @luizscheuer670
    @luizscheuer670 Жыл бұрын

    Why did you show dogs when you said "is given by 3 ingredients"? Did you want to take advantage of some subconscious bias/psychological association that relates to forementioning things we should remember?

  • @hawaslianas
    @hawaslianas7 ай бұрын

    Dude you are good at explaining things I love it But why pause after each sentence !! man you are killing me. long intro!! please work on these things

  • @B_knows_A_R_D-xh5lo
    @B_knows_A_R_D-xh5lo7 күн бұрын

    classics 0:07 0:08 0:08

  • @thepotato7923
    @thepotato7923 Жыл бұрын

    We cannot visualize 4D 'cause we're in 3D world

  • @melancolicodeprofesion5695
    @melancolicodeprofesion5695 Жыл бұрын

    🦦

  • @user-nk4bj9gb4e
    @user-nk4bj9gb4e3 ай бұрын

    bro. way too long introduction. Good video though

  • @Rouwh
    @Rouwh5 ай бұрын

    No story telling at all. Very dry in my opinion

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