Thank you to every one who watched the video and spotted a typo or correction. I will group them in this comment so new viewers can have easy access to them. - At 12:50 by "grad_f and grad_g are inversely proportional", I mean grad_f and grad_g are proportional to each other with a negative coefficients. - At 13:47 , the correct feasibility equation for x is g(x) \le 0, and not g(x) \ge 0 as stated in the video. This typo goes away starting from 15:11

@artashesasoyan6272

2 жыл бұрын

I worked out the gradient by hand (17:00) and found out that our solutions don't match, you have an extra ' - ' (minus sign) in the argument of log. The equation should be : grad[ f(x) - t log( +g(x)) ] and not grad[ f(x) - t log( -g(x)) ]. The gradient of log(g(x)) is grad(g(x))/g(x), no minus sign.

@VisuallyExplained

2 жыл бұрын

@@artashesasoyan6272 Thanks for working this out. Your reasoning would be correct if g were positive, but in this case g

@user-hs1hi9ko1e

8 ай бұрын

At 05:44, P(y) = max u*y subject to u≥0 results in "max{0,...,∞}=∞, if y>0" and "max{-∞,...,0}=0, if y≤0".

@HelloWorlds__JTS

Ай бұрын

It's confusing after 6:46 when you say "u goes first", but that's actually when X "goes" first, etc. You do the same thing again at 9:48, where it is particularly misleading. Love your content! I hope you are somehow finding time to make more. The world could really use more videos giving concise explanations related to convex optimization. I'm particularly interested in manifold learning.

20mins content better than my professor for half a semester. Thank you

you should submit this to 3b1b's summer of math exposition contest

The author must be a genius for making such a great video! Only a man with deep understanding of optimization can explain it virtually

The best video on Lagrangian method that I've ever seen! Great work, thank you!

@VisuallyExplained

2 жыл бұрын

Wow, thanks!

I can't thank you enough for this video and all the content you produce. This has to become the standard for teaching mathematics in schools. It makes everything so much clear, learning becomes so much more efficient. People in education should look at this and reward people like you who innovate and outpeform any classic math teacher. Thank you once again.

Excellent job! This is a new subject for me and it felt really intuitive and interesting all the way through. I hope your channel get the exposure and success that this material deserves.

It is mind blowing to see all these ideas visually. Keep it coming, thank you

Fantastic video! Please keep more coming, these are super-useful! I have actually worked through Boyd's book and the reason I still prefer this is, it's so much quick to refresh your memory with a short video like this. I worked through Boyd's book many years ago and barely remember much now (except that it was fun!).. I suddenly need to recall duality/IP as a quick reference, it's not practical to read that book (or even Boyd's slides). This video is just perfect for that. Another use case I see is, before you deep dive into a convex optimization book, watching this video will give you a great idea and intuition for what's coming next!

@VisuallyExplained

2 жыл бұрын

Thanks, I am glad you find them useful!

What a fantastic series! Thank you so much! Keep up the beautiful work! This is the future of math education at work.

This video is just absoloutely amazing, for anyone just learning optimization. especially the KKT conditions its after 3 months that I have finally understood the actual intuition behind them

Amazing job! I think that in a lot of subjets, there are many encysted text-book explanations , with a bottom-top approach that overwhelms and trap newcomers and practicioners, making this knowledge a specialized tool. Channels like yours unblock that bottleneck, democratizing very useful insights and tools and speeding up progress, thanks!

Amazing visuals with great explanations. I'm so grateful for channels with high quality content like this.

@VisuallyExplained

2 жыл бұрын

Much appreciated! I am glad you liked the channel.

Amazing video, could not understand this for the life of me but this helped tremendously. Videos like this must take a long time to make, but I feel that they will be used for generations. Thank you :)

I have spent a great deal of time trying to understand this topic, and this video series is the single best resource I have ever come across.

@VisuallyExplained

2 жыл бұрын

Thanks. I am really glad it was helpful

I can't wait till this channel explodes and becomes very popular and I can say that I was here in the beginning. Thank you for the amazing content, keep it up!

Your insights and visualizations are immensely helpful!

one of the best series of vids posted on the internet

Thank you so much for putting in all these hours to make a video like that. But it really helped me to understand the topic a lot better!

This magic! How can you represent such difficult concepts so beautifully! This is best youtube video ever

Your explanation is genius! Thank you for taking the time to create such a beautiful explanation. You make learning fun.

Thankyou for this :) I don't think there is a better resource in internet for this topic:) Please keep the videos coming, I already binge watched all of your existing videos, Your way of storytelling is just amazing!

@VisuallyExplained

2 жыл бұрын

Thank you! Will do!

Fantastic video!. You have really motivated the ideas so well and you have beautifully developed the intuition through the narrative. Kudos!

I must say, the insight that the visual approach provided just made it so intuitive. This is quite useful. Keep up the great work.

@VisuallyExplained

2 жыл бұрын

Awesome, thank you!

the way you are presenting equations using animations its amazing sir. even a person with tiny knowledge in math can easily understand it.

The best explanation of the duality problem and KKT condition that I have seen! Thank you

@hyperduality2838

Жыл бұрын

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.

Making a complex math concept simple ... well done!

thanks for the visualization, you made it so simpler for us to understand the problem and also understand what prof said in lecture

In fact, the virtual videos are incredible when it comes to learning new stuff, specially in math problems.

this is the greatest thing I have ever seen! sooo good!!!!

That's the best video i have watched till now. Thanks a lot

Great presentation. You make it so simple...!

Very clear and concise explanation. Thank you so much.

Second time I watch this video, fantastic content! Analogies are a piece of art.

Amazing intuition behind KKT!

Amazing video! Thank you! I hope there will be a lot more optimization videos from you in the future!

Wow! great explanation. This is one topic that I find it intimidating when reading the book, but you explain it beautifully. Keep up the good work man!

@VisuallyExplained

2 жыл бұрын

It's always nice to hear that this was useful, thanks!!

I don’t comment much on yt, but these series are awesome! Thanks and keep us the good work!

thank you , this serie of videos helped me a lot to understand and deepen my knowledge of these concepts. keep up the great work

@VisuallyExplained

2 жыл бұрын

You're very welcome!

These are like how I imagined math lectures would look in the future. Great work, instant sub.

@VisuallyExplained

2 жыл бұрын

Welcome aboard!

Beautifullly explained.

thank you for the amazing background music! It helps me sleep immediately.

Very nice series(and channel in general). I am a big fan of the work of Prof. Boyd, and this series makes the concept very intuitive and nicer to think about. Great work!

@VisuallyExplained

2 жыл бұрын

Thank you, I appreciate that!

elegant explanation! It should be recommended to whoever wants to learn optimization theory.

Awesome and illustrative, thank you.

Great video, one of the best and most intuitive ones I have seen. I think you could have included a short discussion on what does it mean for the multiplier (u or v) to be binding.

Amazing video! Video's like this make me excited to learn, keep it up!

Thank you for this quality content ! Best explanation on this topic

You are just amazing..Thank you so much

Subscribed. Your content is invaluable to CS grad students.

really amazing videos, visually and intuitively explanation are really important to me, thank you for doing these great videos

Exceptional video.... It's so clear Bravo.

you put soo much effort. subscribed right away!!

Very helpful stuff! Thank you very much for your effort.

It was genuinely helpful. Thank you for the insightful teaching

I've finally known where the hell Lagrangian comes from Such a great video

Such a beautiful video. Thanks a ton for this

Awesome video, thanks for make this available.

Why I can only give one like to this video?! This video is awesome!!! Thanks for making it!

Wonderfully explained, I am in awe

@VisuallyExplained

2 жыл бұрын

Happy to hear that!

Thank you very much for this video!! I'm just getting started with semidefinite programming

Holy?! The NIP derivation makes so much sense!!

Very well explained! Tbarkllah elik

Awesome explanation! keep these videos up...

Amazing exposiotion! Thanks a lot and it really helps me!

absolutely outstanding! thank you so much. as a discrete algorithm designer unexpectedly thrown into the trenches of solving a difficult bi-level mixed-integer linear optimization problem, this was very intuitive and much less scary than the Wikipedia article.

@VisuallyExplained

2 жыл бұрын

Yay, glad this was helpful!

brilliantly explained, thanks a ton

Hello Bachir! , This is so amazing ! I can just say - god bless you !!! Best Duality explanation so far !!

@VisuallyExplained

2 жыл бұрын

Thanks a lot!!!

@hyperduality2838

Жыл бұрын

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.

Great video. Thank you

amazing video!!! Thank you!

BEAUTIFUL!!!

Very helpful video!!! Thank you very much

Brilliant effort!

Just sth aside but I really like the background music. Gives me a sense of calm and peace for learning.

Great Video and explanation.

thanks mate. was having some doubts after going through Boyd's book... now many things are clear

@VisuallyExplained

2 жыл бұрын

You are most welcome

Very well explained

This video is amazing, thanks!

Pure Gold!

Love the video! Student should really start from your video than the standard textbooks!!!!!!

My professor did teach quite well but I'm missing some intuitive visualizations. All makes sense now thanks to your video!

I absolutely love this!!! It's so good! please keep on making videos like this! Is there any way you could be persuaded to make 4 to 5 small assignments to each video? Maybe just for patrons or something like that?

Thank you so much for this amazing video 💯

@VisuallyExplained

2 жыл бұрын

My pleasure!

excellent video! Thanks you so much!

thank you so much for the great video. You saved me from hours of reading on text book but not understand anything

Excellent! Really helpful

Thank you for this great explanation

@VisuallyExplained

2 жыл бұрын

Glad it was helpful!!

Omg absolutely amazing

Thank you so much, it helps me a lot.

This is amazing!!! thanks!!!

Great video! Thank you so much!!!

@VisuallyExplained

2 жыл бұрын

Glad you enjoyed it!

Wonderful Video! It helped so much

@VisuallyExplained

2 жыл бұрын

Yaay!

Great video

That was a very nice presentation and a lot of fun to watch! ps: Maybe you could also make a video on the duality gap and Slater's condition?

🎯 Key Takeaways for quick navigation: 00:00 🧠 *Convex optimization problems involve minimizing convex objective functions subject to constraints. Duality provides a useful perspective in solving such problems efficiently.* 01:27 🚢 *In a practical example of ship navigation, convex optimization is applied to minimize the objective function while considering constraints, turning it into a convex optimization problem.* 03:20 🔄 *Introducing a penalty function helps eliminate constraints, but choosing an appropriate penalty function is crucial. The "zero-infinity" penalty function is one such example.* 05:54 🔄 *Penalty functions can be approximated with linear penalties. The max of these linear penalties transforms the problem into a min-max problem, introducing the concept of dual problems.* 08:59 🔄 *Deriving the dual problem involves introducing Lagrangian multipliers, leading to a lower bound on the optimal value of the primal problem, establishing strong duality under certain assumptions.* 10:36 🎓 *The Karush-Kuhn-Tucker (KKT) conditions are essential in convex optimization, providing necessary conditions for optimality, with feasible solutions satisfying a set of equations and inequalities.* 14:29 ⚙️ *The KKT conditions reduce solving an optimization problem to solving equations and inequalities, facilitating the development of general-purpose optimization solvers.* 16:22 🔄 *The interior point method perturbs the KKT conditions to make them easier to solve, using a parameter "t" that is gradually reduced. It leverages two key insights to navigate the perturbed conditions efficiently.* 20:54 🔄 *The interior point method follows the "central path," gradually moving towards smaller "t" values until it reaches the solution. The central path stays within the interior of the feasible region, justifying the method's name.* Made with HARPA AI

20min better than a whole 1hour lecture from my professor

this video is amazing

Awesome!

Thnak you so much for this video, it's so nice:)

@VisuallyExplained

2 жыл бұрын

You're welcome 😊

Thanks a lot man!