@shuinemu
20mins content better than my professor for half a semester. Thank you
@ulissemini5492
you should submit this to 3b1b's summer of math exposition contest
@YuxuanHarry
The author must be a genius for making such a great video! Only a man with deep understanding of optimization can explain it virtually
@pej47
The best video on Lagrangian method that I've ever seen! Great work, thank you!
@gtorres94
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.
@apaarsadhwani
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!
@gamestudywithkoi
🎯 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
@meeseeks1489
This magic! How can you represent such difficult concepts so beautifully! This is best youtube video ever
@manojpawar9688
Falling short of words, but with whatever limited vocabulary I have, let me say this is gem of a video. I was struggling with Lagrangian, primal, dual, min, max concepts and you have explained it extremely beautifully. Thanks a ton !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
@aashishchauhan1989
It is mind blowing to see all these ideas visually. Keep it coming, thank you
@DevRajyaguru-lx8pi
Hello, I'm coming from the control theory background. I have been struggling to understand the purpose of KKT for a long time. This video is so clearly explained I just got it. I just it in one time look! Thank you so much. I would love more on optimization series.
@letteringby_sara
This video deserves millions of views and likes! such a beautiful example, the visuals, the explanation, everything is on point. This is the only video that has helped me understanding the Langragian method. Thank you so much, keep on making such amazing content!
@cowkeydev
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 :)
@MintaoYE
The best explanation of the duality problem and KKT condition that I have seen! Thank you
@l10n919
This is an excellent explanation of this subject. Last year I took an Intro to Optimization course at my university and had to fight tooth and nail to get the grade I wanted. This trilogy has really increased my intuition on the subject and helped me better understand the more complex math behind KKT and other optimality math theorems which you omitted in this video. Thanks!
@ElectronsSoul
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.
@govindchari4586
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.
@alirezaasghari4547
In fact, the virtual videos are incredible when it comes to learning new stuff, specially in math problems.
@林泓均-q4j
Why I can only give one like to this video?! This video is awesome!!! Thanks for making it!
@VisuallyExplained