lol, I went to 3Blue1Brown to see if Grant had any videos explaining what the langrange multipliar and lagrangians are.... seeing not I head over to Khan Academy... and Grant is teaching the lesson
Went from Constrained Optimization Introduction to this video. Absolutely love the clear explanation w/ the graphs! No idea why other materials have to make it so hard to understand.
Needed to pick up some basic know how about lagrangian in order to work through a proof regarding partition functions. And I was worried it was going to take me forever considering other texts I have aren't particularly clear and I didn't take lagrangian in undergrad. But oh my, this series is short, snappy, to the point and intuitive. Your tutorials are timeless and a gift to humanity. Thank you.
@@jairjuliocc I was talking about the famous Real Business Cycle model in macroeconomics. When you are working with factors of production like labor and capital and you need Utility maximisation in a single period RBC model. The first order condition equations for capital and labor need a lagrange multiplier. If you are not a student of finance and economics, these will go over your head. And if you have studied macroeco, then these will be the most basic thing you learn.
Many thanks! I learned about lagrange multipliers as of yesterday, but it's been rather difficult to understand just exactly what it is even thought the math makes sense - your video clarified for me. Thanks again
It's a good refresher. Thanks. I would like to request you for advance math courses. You are very good at teaching. I watched your linear algebra playlist and also subscribed to your youtube (3Blue1Brown). It's awesome: How about abstract algebra, or even number theory. Thanks
thanks a lot, great video ... I watched a few videos on Lagrange multipliers and this is the best so far ... it would be great if there were links to the previous and next video in the series
Woah what! I was not expecting that lambda had some meaning! Oh why didn't my Calc 3 classes show me this. I don't even believe this was in my Calc 3 textbook, or maybe perhaps it was burried in some of the problems at the end of the Lagrange Multiplier section.
How do we know that when the gradients are parallel, it's an extremum of the constraint g(x,y), rather than an inflection point? For example, extremising the paraboloid f(x,y) = x² +y² subject to y = 2x³ + 1. The gradients are parallel at (0,1), but this does not extremise the function f subject to the constraint g(x,y). Also, can I request a video on Lagrange multipliers with multiple constraints? This is much harder to find. I'm particularly interested in its use in deriving the Boltzmann distribution as maximising the number of micro states subject to constant molecule number and total energy. Also, a video on how this relates to Lagrangian or Hamiltonian mechanics would be fantastic and a common application I think.
Wouldn't we suspect, just from looking at the parallel gradients of R and B, that for every small increase of B you get λ times an increase of R? I mean something like λ = |grad R|/|grad B| = dR/dB on a curve perpendicular to the two tangent contour lines -same as Anton Geraschenko says below, but more visually intuitive, I think. (I admit that you still have to believe that any variation of h and s should be along that perpendicular curve, but that is how you keep R and B contours tangent to each other)
In a previous video it has been explained. You have to calculate the tangent of the two function and they have to be proportional to each other. The propionality constant is lambda.
Why can’t you just solve for h or s in one function and substitute that expression in the other function? Then you can just set the derivative to 0 to find the optimization.
That's not always possible. If say, your constraint function was not factorizable e.g. xsin(y) + yx^2=1. In this case, you can't express x in terms of y or the other way around and substitute that in f(x)
Because you made them so through the Lagrange multiplier. There are multiple grads of the contour of the function that don't have a proportional grad with the constraint, but by assuming that they are (and that they relate to each other through the Lagrande multiplier), you can solve the system of equations and get all the points at which your previous assumption, that the two gradients are proportional, is true.
Shaelyne Collorone Okay, I understand this. But why don't you just go on the website www.khanacademy.com and look for what you need instead of clicking on videos you don't want to see?
![Seungmin "그렇게, 천천히, 우리(As we are)" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/kAzmhLHePqU/mqdefault.jpg)
lol, I went to 3Blue1Brown to see if Grant had any videos explaining what the langrange multipliar and lagrangians are.... seeing not I head over to Khan Academy... and Grant is teaching the lesson
Two years later, I did the exact same thing.
@@Jurgan6 2 months later, here I am, having done the same thing :')
@@brandontay2053 2 weeks later, mee too!!
me too
@@YashPatel-vt8or which college bro 😂
Went from Constrained Optimization Introduction to this video. Absolutely love the clear explanation w/ the graphs! No idea why other materials have to make it so hard to understand.
My theory is they either don't actually understand the topic, or they are gate-keeping
Needed to pick up some basic know how about lagrangian in order to work through a proof regarding partition functions. And I was worried it was going to take me forever considering other texts I have aren't particularly clear and I didn't take lagrangian in undergrad. But oh my, this series is short, snappy, to the point and intuitive. Your tutorials are timeless and a gift to humanity. Thank you.
good Lord this video brought so much understanding to the LaGrange multiplier it´s insane. God bless you Sir
Last time I checked I am studying how to minimize Optimum Margin Classifier for Support Vectors, now I am here, I don't know how, but I love it.
I knew Lagrange Optimization since long time. But NOW I can claim understand it perfectly!
Thank you so much!
9:50 I believe what you meant was “let’s pause and ponder...” right ? Yeah, you can’t fool us, we know it was you lecturing, 3Blue1Brown.
This is important in economics. One of the major concepts in Real business cycle.
I know im a little late but, Can you explain more?
@@jairjuliocc I was talking about the famous Real Business Cycle model in macroeconomics. When you are working with factors of production like labor and capital and you need Utility maximisation in a single period RBC model. The first order condition equations for capital and labor need a lagrange multiplier. If you are not a student of finance and economics, these will go over your head. And if you have studied macroeco, then these will be the most basic thing you learn.
@@tunim4354 wow you replied after 4 years
@@Leo-tf3rw AHAHHAHAH he did
That person probably already finished college
9:31 I thought most of the things in math comes from nowhere until I got your videos.
Many thanks! I learned about lagrange multipliers as of yesterday, but it's been rather difficult to understand just exactly what it is even thought the math makes sense - your video clarified for me. Thanks again
Nice. It would have been helpful if you had a link to the next video or the play list in the description.
"Hours of Labor and Tons of Steel". That sounds like a rejected thrash metal album.
SuperIdiotMan00 that honestly made me laugh out loud
man, thats what i call a joke
lmaooo
Thank you Khan Academy!
It's a good refresher. Thanks. I would like to request you for advance math courses. You are very good at teaching. I watched your linear algebra playlist and also subscribed to your youtube (3Blue1Brown). It's awesome: How about abstract algebra, or even number theory. Thanks
Riken Maharjan I second this!
no such thing as gx or not
thanks a lot, great video ... I watched a few videos on Lagrange multipliers and this is the best so far ... it would be great if there were links to the previous and next video in the series
I totally agree.
how to find "the previous video" there is no playlist linked to the video
The voice sounds familiar. Is this the guy from the 3blue1brown channel? Anyway, this is very well explained.
Woah what! I was not expecting that lambda had some meaning! Oh why didn't my Calc 3 classes show me this. I don't even believe this was in my Calc 3 textbook, or maybe perhaps it was burried in some of the problems at the end of the Lagrange Multiplier section.
How do we know that when the gradients are parallel, it's an extremum of the constraint g(x,y), rather than an inflection point? For example, extremising the paraboloid f(x,y) = x² +y² subject to y = 2x³ + 1. The gradients are parallel at (0,1), but this does not extremise the function f subject to the constraint g(x,y).
Also, can I request a video on Lagrange multipliers with multiple constraints? This is much harder to find. I'm particularly interested in its use in deriving the Boltzmann distribution as maximising the number of micro states subject to constant molecule number and total energy. Also, a video on how this relates to Lagrangian or Hamiltonian mechanics would be fantastic and a common application I think.
Really helpful to help me get a thorough understanding
In what playlist does constraint programming topics it belongs?
Wouldn't we suspect, just from looking at the parallel gradients of R and B, that for every small increase of B you get λ times an increase of R? I mean something like λ = |grad R|/|grad B| = dR/dB on a curve perpendicular to the two tangent contour lines -same as Anton Geraschenko says below, but more visually intuitive, I think. (I admit that you still have to believe that any variation of h and s should be along that perpendicular curve, but that is how you keep R and B contours tangent to each other)
At 4:30, why we are taking gradient of L(Lagrangian function) = 0? Can anyone please put some light on this. Thanks!
In a previous video it has been explained. You have to calculate the tangent of the two function and they have to be proportional to each other. The propionality constant is lambda.
Wouldn't the contour of B be pointed down,, from the concavity? Or is the multiplier acting as a "negative" scalar, flipping it around?
Which playlist is this in?
So is the lagrange multiplier also considered an eigenvalue?
this is fantastic point !
If does not ask for the maximum ( or minimum), how can you know it is indeed the maximum (or minimum) value???
So elucidating
thanks😁🏅
The one who can not learn is because he doesn't want 💯
Anybody knows a book of Multivariable Calculus' history? Please help me.
wow...Thanx a lot!!
6:47 REALLY!!!
I love you grant.
I think I need some more animations to understand this.
Finally I got it
guys can the lamda be equal to 0 ?
Yeah but wouldn't that just mean our constraint has no impact on our ability to optimize R?
Why can’t you just solve for h or s in one function and substitute that expression in the other function? Then you can just set the derivative to 0 to find the optimization.
That's not always possible. If say, your constraint function was not factorizable e.g. xsin(y) + yx^2=1. In this case, you can't express x in terms of y or the other way around and substitute that in f(x)
oh
Commenting to spread on the tubes!
I like it
I don't see why the two fradient are propotinal
Because you made them so through the Lagrange multiplier. There are multiple grads of the contour of the function that don't have a proportional grad with the constraint, but by assuming that they are (and that they relate to each other through the Lagrande multiplier), you can solve the system of equations and get all the points at which your previous assumption, that the two gradients are proportional, is true.
F**k, This is GOLD.
❤
Argh why no inequality constraints
first like
3blue one brown guy
i dont like that he speaks so fast
While you maximize your revenue, I'll be maximizing my profit... ;)
Omg
why sending math i'm not needing ?
Maybe just don't click videos you do not need to see?
iii 3xki they sending a different kind of math i don't need.
Shaelyne Collorone
Okay, I understand this. But why don't you just go on the website www.khanacademy.com and look for what you need instead of clicking on videos you don't want to see?
@@shellycollorone3703 who is they