Meaning of Lagrange multiplier

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In the previous videos on Lagrange multipliers, the Lagrange multiplier itself has just been some proportionality constant that we didn't care about. Here, you can see what its real meaning is.

[@8bit_pineapple]

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

[@Jurgan6]

Two years later, I did the exact same thing.

[@brandontay2053]

@@Jurgan6 2 months later, here I am, having done the same thing :')

[@morancium]

@@brandontay2053 2 weeks later, mee too!!

[@YashPatel-vt8or]

me too

[@morancium]

@@YashPatel-vt8or which college bro 😂

[@sjwang3892]

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.

[@technosapien330]

My theory is they either don't actually understand the topic, or they are gate-keeping

[@dirkjensen935]

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.

[@DefinitelyNotNhanTho]

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.

[@masterchief8646]

good Lord this video brought so much understanding to the LaGrange multiplier it´s insane. God bless you Sir

[@leeris19]

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.

[@mehdij9494]

I knew Lagrange Optimization since long time. But NOW I can claim understand it perfectly! Thank you so much!

[@phil97n]

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

[@SuperIdiotMan00]

"Hours of Labor and Tons of Steel". That sounds like a rejected thrash metal album.

[@christianaustin782]

SuperIdiotMan00 that honestly made me laugh out loud

[@alekseivoronov3763]

man, thats what i call a joke

[@Ferdinaand]

lmaooo

[@tunim4354]

This is important in economics. One of the major concepts in Real business cycle.‎

[@jairjuliocc]

I know im a little late but, Can you explain more?

[@tunim4354]

@@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.

[@Leo-tf3rw]

@@tunim4354 wow you replied after 4 years

[@hbbh]

@@Leo-tf3rw AHAHHAHAH he did

[@hbbh]

That person probably already finished college

[@rikenm]

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

[@justinward3679]

Riken Maharjan I second this!

[@zes7215]

no such thing as gx or not

[@michaeljpchen6469]

Really helpful to help me get a thorough understanding

[@pritomroy2465]

9:31 I thought most of the things in math comes from nowhere until I got your videos.

[@alexanderherbertkurz]

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

[@whetstoneguy6717]

I totally agree.

[@ThePiMan0903]

Thank you Khan Academy!

[@dionsilverman4195]

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.

[@kawhiknot1016]

In what playlist does constraint programming topics it belongs?

[@umountable]

how to find "the previous video" there is no playlist linked to the video

[@franks.6547]

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)

[@abdullahalmosalami2373]

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.

[@xiaoweidu4667]

this is fantastic point !

[@supreme84x]

Wouldn't the contour of B be pointed down,, from the concavity? Or is the multiplier acting as a "negative" scalar, flipping it around?

[@liabraga4641]

So elucidating

[@abhishek_sengupta]

wow...Thanx a lot!!

[@animeshpuzari8235]

thanks😁🏅

[@CalleTful]

Which playlist is this in?

[@RajatGoel1]

6:47 REALLY!!!

[@usamsersultanov689]

Finally I got it

[@sam4395]

oh

[@Rockyzach88]

So is the lagrange multiplier also considered an eigenvalue?

[@arslanhojiyev5996]

If does not ask for the maximum ( or minimum), how can you know it is indeed the maximum (or minimum) value???

[@miguelangelhernandezortiz7303]

Anybody knows a book of Multivariable Calculus' history? Please help me.

[@dagia3209]

I like it

[@johncharles3907]

I think I need some more animations to understand this.

[@Postermaestro]

Commenting to spread on the tubes!

[@Skandalos]

The voice sounds familiar. Is this the guy from the 3blue1brown channel? Anyway, this is very well explained.

[@ruSEXtreme]

why should the 2 gradients have to be proportional, as opposed to being equal to each other? if they're not equal at the point of contact, then theyre not tangent to each other..?

[@BillPickle]

so long as the direction is the same, the gradient vectors will be parallel scalar multiples (lambda). The magnitudes of the vectors do not matter, and if reduced to unit vectors, would be identical.

[@indranilroy691]

At 4:30, why we are taking gradient of L(Lagrangian function) = 0? Can anyone please put some light on this. Thanks!

[@dsanjoy]

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.

[@atriagotler]

I love you grant.

[@mv3845]

❤

[@buh357]

F**k, This is GOLD.

[@jullevv]

first like

[@Majestic469]

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.

[@MayankGoel447]

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)

[@alaypal7484]

Omg

[@elgodyr2683]

guys can the lamda be equal to 0 ?

[@goclbert]

Yeah but wouldn't that just mean our constraint has no impact on our ability to optimize R?

[@theacademyofgermanidealism6210]

3blue one brown guy

[@anas.2k866]

I don't see why the two fradient are propotinal

[@hectorbetancourt2854]

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.

[@uvenga]

The one who can not learn is because he doesn't want 💯

[@tag_of_frank]

Argh why no inequality constraints

[@tadasvaitkevicius5799]

i dont like that he speaks so fast

[@Jmtri7]

While you maximize your revenue, I'll be maximizing my profit... ;)

[@shellycollorone3703]

why sending math i'm not needing ?

[@zayedalsuwaidi7697]

Maybe just don't click videos you do not need to see?

[@shellycollorone3703]

iii 3xki they sending a different kind of math i don't need.

[@zayedalsuwaidi7697]

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?

[@edjrage7745]

@@shellycollorone3703 who is they