Convexity and The Principle of Duality

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  • เผยแพร่เมื่อ 25 พ.ย. 2024

ความคิดเห็น • 80

  • @snailscout9383
    @snailscout9383 2 ปีที่แล้ว +95

    I feel fortunate to live in a time were there are people who teach hard-to-understand concepts for free in a easy to grasp fashion. Hats off to you and thank you a lot

    • @hyperduality2838
      @hyperduality2838 2 ปีที่แล้ว +1

      From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
      According to the 2nd law of thermodynamics all observers have a syntropic perspective.
      My syntropy is your entropy and your syntropy is my entropy -- duality!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
      Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
      Teleological physics (syntropy) is dual to non teleological physics (entropy).
      Duality creates reality.
      "Always two there are" -- Yoda.
      Points are dual to lines -- the principle of duality in geometry.

  • @nodirbek3272
    @nodirbek3272 25 วันที่ผ่านมา +1

    I enjoyed this video like participating in an exciting show program. I didn't even have to stress my brain to visualize such complex concepts like multivariable functions.

  • @Sirentuber
    @Sirentuber ปีที่แล้ว +3

    Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.

  • @katherineadams5824
    @katherineadams5824 3 วันที่ผ่านมา

    Brilliant! Wish these concepts were explained in this intuitive way during my PhD.

  • @virmaq5187
    @virmaq5187 2 ปีที่แล้ว +6

    As a visual learner, this video helped me tremendously. Thank you!

  • @raulsena3917
    @raulsena3917 3 ปีที่แล้ว +8

    Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!

  • @jiaqi9113
    @jiaqi9113 3 ปีที่แล้ว +15

    Extremely good introduction!!!! It is very hard to imagine how much work put behind the video!! Thanks for your input on this!!
    I already worked on convex optimization problem in a research project for a few months but honestly I really don't know what is special about convex optimization. Thanks for giving us the intuition behind it!!

    • @hyperduality2838
      @hyperduality2838 2 ปีที่แล้ว

      From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
      According to the 2nd law of thermodynamics all observers have a syntropic perspective.
      My syntropy is your entropy and your syntropy is my entropy -- duality!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
      Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
      Teleological physics (syntropy) is dual to non teleological physics (entropy).
      Duality creates reality.
      "Always two there are" -- Yoda.
      Points are dual to lines -- the principle of duality in geometry.

  • @wexwexexort
    @wexwexexort ปีที่แล้ว +3

    I always like to watch the visual explanations even though I know the topic quite well and to be honest, you do a really good job on both explanations and visuals.

  • @parahumour4619
    @parahumour4619 11 หลายเดือนก่อน +1

    Amazing video, your channel deserves more views. I would suggest having a section where you ask the viewers questions so they stop and think and end up being onboard with the understanding

  • @vats6
    @vats6 3 ปีที่แล้ว +3

    Woah! Thanks a lot sir, for such an intutive explaination of convexity. The best explaination I have seen on the internet so far!

    • @hyperduality2838
      @hyperduality2838 2 ปีที่แล้ว

      From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
      According to the 2nd law of thermodynamics all observers have a syntropic perspective.
      My syntropy is your entropy and your syntropy is my entropy -- duality!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
      Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
      Teleological physics (syntropy) is dual to non teleological physics (entropy).
      Duality creates reality.
      "Always two there are" -- Yoda.
      Points are dual to lines -- the principle of duality in geometry.

  • @colin_hart
    @colin_hart 2 ปีที่แล้ว +4

    The code samples for linear programming and least squares are swapped at 0:23.
    I’ve been enjoying your work. Thanks for sharing!

    • @VisuallyExplained
      @VisuallyExplained  2 ปีที่แล้ว +1

      Thanks for watching carefully, and I am glad you liked my videos. :-)

  • @rubenosmond8200
    @rubenosmond8200 ปีที่แล้ว

    Thank you sir. I'm having a hard time understanding this concept for my machine learning class and you helped me in a beautiful fashion. May you have great things in line.

  • @cmatiolli13
    @cmatiolli13 2 ปีที่แล้ว +2

    Your videos are awesome. The right balance of math concepts and intuition to explain complex ideas is the perfect fit for this essential concept.

    • @hyperduality2838
      @hyperduality2838 2 ปีที่แล้ว

      From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
      According to the 2nd law of thermodynamics all observers have a syntropic perspective.
      My syntropy is your entropy and your syntropy is my entropy -- duality!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
      Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
      Teleological physics (syntropy) is dual to non teleological physics (entropy).
      Duality creates reality.
      "Always two there are" -- Yoda.
      Points are dual to lines -- the principle of duality in geometry.

  • @gustavgille9323
    @gustavgille9323 5 หลายเดือนก่อน

    The least squares error example is beautiful!!!

  • @imotvoksim
    @imotvoksim 2 ปีที่แล้ว +3

    The least squares example you show at 7:59 has a wrong sign as far as I can tell!.Otherwise a great video providing the intuition I was looking for, took down some notes, hopefully they finally stick and I understand this dual magic once and for all, thanks!

    • @VisuallyExplained
      @VisuallyExplained  2 ปีที่แล้ว +3

      You are correct about the wrong minus sign, thanks for watching the video carefully, and thank you for the very nice comment. I am glad the video was helpful to you. :-)

  • @parhamzolfaghari7394
    @parhamzolfaghari7394 ปีที่แล้ว +1

    Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.

  • @SonLeTyP9496
    @SonLeTyP9496 3 ปีที่แล้ว +4

    Awesome :) cant wait to see next episode :D

  • @phogbinh
    @phogbinh 2 ปีที่แล้ว

    God like overview of the topic. Thank you.

  • @MaxWasserman1
    @MaxWasserman1 3 ปีที่แล้ว +5

    Huge fan. Keep it up.

  • @ian.ambrose
    @ian.ambrose ปีที่แล้ว

    Yes! New Blender tutorial!

  • @thebifrostbridge3900
    @thebifrostbridge3900 2 ปีที่แล้ว

    Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"

  • @Mewgu_studio
    @Mewgu_studio ปีที่แล้ว

    I learnt so much from this video, I love you so much

  • @박시연-m2m
    @박시연-m2m ปีที่แล้ว +3

    great video! What program did you use to make this fantastic visualization?

  • @lilialola123
    @lilialola123 ปีที่แล้ว

    AMAZING visualizations, thank you

  • @think9824
    @think9824 3 ปีที่แล้ว +4

    very interesting and useful. thanks a lot

  • @jsalca52
    @jsalca52 3 ปีที่แล้ว +1

    Shokran kathir!

  • @ZhanCaitao
    @ZhanCaitao 2 ปีที่แล้ว +1

    Great video!

  • @mandystritzke3339
    @mandystritzke3339 3 ปีที่แล้ว +1

    Great explanation!

  • @nashwahammoud4076
    @nashwahammoud4076 8 หลายเดือนก่อน

    That's wonderful 🎉 thanks for you

  • @chinmaydhole4001
    @chinmaydhole4001 2 ปีที่แล้ว

    mind blown! thanks a lot for this video

  • @jameskirkham5019
    @jameskirkham5019 6 หลายเดือนก่อน

    Amazing video thank you

  • @AJ-et3vf
    @AJ-et3vf ปีที่แล้ว

    awesome video. thank you

  • @LuisLascanoValarezo
    @LuisLascanoValarezo ปีที่แล้ว

    7:59 Formula is key for interviews and in Machine Learning

  • @fabricetshinangi5042
    @fabricetshinangi5042 3 ปีที่แล้ว

    Amazing video, thank you for the explanation

    • @VisuallyExplained
      @VisuallyExplained  3 ปีที่แล้ว

      Glad it was helpful!

    • @fabricetshinangi5042
      @fabricetshinangi5042 3 ปีที่แล้ว +2

      Yes it is very insightful. I'm actually optimizing a Non linear cost function (with more than 6 variables) using newton raphson method. And my hessian matrix must be >=0

  • @AranTodd
    @AranTodd 15 วันที่ผ่านมา

    Thanks for the forecast! Could you help me with something unrelated: My OKX wallet holds some USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). What's the best way to send them to Binance?

  • @sateeshk3347
    @sateeshk3347 2 ปีที่แล้ว

    Great Video, thank you for the effort and time in creating the same.

  • @federicobarra3655
    @federicobarra3655 2 ปีที่แล้ว

    amazing explanation! keep it up!

  • @olivier306
    @olivier306 2 ปีที่แล้ว

    beautiful

  • @wokeclub1844
    @wokeclub1844 2 ปีที่แล้ว +1

    Great video!!
    Can Someone please explain How at 3:11 the equality Can be considered as those two inequalities?

    • @VisuallyExplained
      @VisuallyExplained  2 ปีที่แล้ว +1

      sure, let's take an example. The equality x = 1 is equivalent to x >= 1 and x

  • @_soundwave_
    @_soundwave_ ปีที่แล้ว

    What about convex in terms of geometry? What about all three definition of convexity with that of geometry?

  • @benjaminbenjamin8834
    @benjaminbenjamin8834 2 ปีที่แล้ว

    I appreciate this video but there was nothing related to primal and dual concepts in this video?

  • @osamazaheer6430
    @osamazaheer6430 3 ปีที่แล้ว

    great. Thanks

  • @werdasize
    @werdasize 2 ปีที่แล้ว +1

    Really nice! But one thing I didn’t understand was at 5:02 ish. You say that the intersection of those support planes is the convex set.. but in your example, isn’t the intersection of the planes just a bunch of connected lines? Not sure if I understood correctly.

    • @werdasize
      @werdasize 2 ปีที่แล้ว

      Or is it that there exists an infinite set of unique such planes whose intersection is the surface of the convex set? Even then, still not sure how to recover the interior.

    • @VisuallyExplained
      @VisuallyExplained  2 ปีที่แล้ว +1

      Great observation. The intersection of the hyperplanes themselves could be empty. It is the intersection of the corresponding half spaces that gives the convex set.

    • @werdasize
      @werdasize 2 ปีที่แล้ว

      @@VisuallyExplained makes perfect sense then, thanks!!

  • @tomwassing
    @tomwassing 3 ปีที่แล้ว

    Absolutely amazing video! Great visualisation and explanation of the topic. I found it pretty difficult to find any interactive and visual content, thank you! I just finished my computer science bachelor and I find a great interest in these types of problems, could you recommend me an introductory book?

    • @VisuallyExplained
      @VisuallyExplained  3 ปีที่แล้ว +1

      Awesome! Convex Optimization by Boyd and Vandenberghe is really good. The first author has his lectures on youtube as well if you're interested.

    • @hyperduality2838
      @hyperduality2838 2 ปีที่แล้ว

      @@VisuallyExplained From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
      According to the 2nd law of thermodynamics all observers have a syntropic perspective.
      My syntropy is your entropy and your syntropy is my entropy -- duality!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
      Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
      Teleological physics (syntropy) is dual to non teleological physics (entropy).
      Duality creates reality.
      "Always two there are" -- Yoda.
      Points are dual to lines -- the principle of duality in geometry.

  • @rylanschaeffer3248
    @rylanschaeffer3248 3 ปีที่แล้ว +2

    You have an extra negative at 7:59, I think.

    • @VisuallyExplained
      @VisuallyExplained  3 ปีที่แล้ว +2

      Correct! I will compile a list of typos and add it to the description. Thank you!

  • @Tibug
    @Tibug ปีที่แล้ว +1

    These videos are marvelous(!) but you need a better mic.

  • @aswathik4709
    @aswathik4709 2 ปีที่แล้ว

    6:51 is the lhs f(x)?

  • @VivekYadav-ds8oz
    @VivekYadav-ds8oz 8 หลายเดือนก่อน

    I don't get how h(x)

  • @dempstert2712
    @dempstert2712 2 ปีที่แล้ว

    At 3:12, did you mean to say hᵢ(x)≤ 0 and -hᵢ(x) ≥ 0 ?
    Such that the overlap of the two functions is linear?

    • @VisuallyExplained
      @VisuallyExplained  2 ปีที่แล้ว

      "hᵢ(x)≤ 0" and "-hᵢ(x) ≥ 0" are actually the same thing.

  • @RahulGoyal-or1ht
    @RahulGoyal-or1ht 5 วันที่ผ่านมา

    Local minima will be global minima what about local maxima? Will it also be global maxima?

  • @sygmermartins6082
    @sygmermartins6082 3 ปีที่แล้ว

    very nice :)

  • @hyperduality2838
    @hyperduality2838 2 ปีที่แล้ว

    From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics.
    According to the 2nd law of thermodynamics all observers have a syntropic perspective.
    My syntropy is your entropy and your syntropy is my entropy -- duality!
    Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
    Homology (convergence, syntropy) is dual to co-homology (divergence, entropy).
    Teleological physics (syntropy) is dual to non teleological physics (entropy).
    Duality creates reality.
    "Always two there are" -- Yoda.
    Points are dual to lines -- the principle of duality in geometry.

  • @blueberry23
    @blueberry23 8 หลายเดือนก่อน

  • @Throwingness
    @Throwingness 2 ปีที่แล้ว

    Who named the friggin things 'primal' and 'dual'? It's confusing. 'Primal' is fine. 'Dual' makes it sound like we're dealing with two more of something. As we have three now.

  • @korayyy440
    @korayyy440 2 ปีที่แล้ว

    >Potato shape
    >Makes an egg

  • @eneserdogan34
    @eneserdogan34 2 ปีที่แล้ว

    This is some serious gourmath shit.

  • @himanshuverma298
    @himanshuverma298 8 หลายเดือนก่อน

    Bhai please be accurate

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    @tsunningwah3471 4 หลายเดือนก่อน

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    @tsunningwah3471 11 หลายเดือนก่อน

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    @tsunningwah3471 4 หลายเดือนก่อน

    zbian