Constrained optimization introduction

[@alexanderherbertkurz]

your animations are beautiful ... when I studied this 30 years ago nothing like this was available ... I can't tell you how much I enjoy going through this now again ... thanks so much

[@preetkanwalsingh3532]

13 textbook authors are upset at how informative this series is!

[@WeissForlorn]

3Blue1Brown is great

[@suryahr307]

I only found this video. Could you share link of whole series/Playlist please

[@TheDroidMate]

They dont want you to know ..

[@samsungn1021]

Sc Aggarwal

[@RoyalYoutube_PRO]

@@suryahr307 Search for multivariable calculus by khan academy

[@alijavadyfar3778]

truth be told, I've been using this method for solving optimization problems for some 6 years now, but I understood the concept only after I watched this playlist. MOST INFORMATIVE EVER !

[@robertwilsoniii2048]

Grant you are the man. You are making my startup possible.

[@Alley00Cat]

The voice is actually strangely close Khan's. I was confused at first. Awesome video!

[@bunkerputt]

Alley00Cat Khan repeats when he writes.

[@rishabhbhardwaj2873]

This guy is a legend!

[@jamesgoodman5102]

I just realised you're 3Blue1Brown from the sound of your voice. Nice to see you on different channels :)

[@EDUARDO12348]

Good voice recognition system you got, I didn't make that connection at first but I think you are right.

[@kalyanitewari]

His visuals say it too!

[@hakeemnaa]

5:56 the blue line ( contour) represents the z-axis or the height ( each line represents same height or z value or the output of f(x,y) so we need the max value but it must touch the circle ( touch= tangent), if it is not tangent, f will intersect the circle with two points which mean there will be a point between this point which has more f ( height, or z value)

[@Tomahawk1999]

mathematics when explained this way is actually much more interesting.

[@ufkun20]

And less confusing

[@rayknn]

You think it is. I prefer the books tho. I use these video's as an extra way of checking my knowledge about a certain subject.

[@TheDroidMate]

When the two most appreciated educators team up. 😍

[@ericbischoff9444]

There would be (in this pecular case) a trick to make this a single-variable calculus problem : replace x with cos t and y with sin t, and whoops, you're done, the problem is now to maximize a function of t :-)

[@Prism684]

What an explanation!!! Marvelous. Starting from visualization going to formulation to algebraic equation to solve. You are amazing!!! Do I need to read thick book?? No. This is the time of fast learning and get on with action

[@huynjinful]

I always enjoy your videos. In terms of this kind of math videos, however, i wish videos are aligned sorted under the categories ;)

[@shkittle07]

This couldn't be more important at a time like this. #COVID19

[@Heisenberg8307]

Whoa...this guy's voice sounds gentle now completely different from Linear Algebra videos...i like the old voice better.

[@alfcnz]

Why there is no link to a playlist???

[@SohamChakraborty42069]

We could think of parameterizing the given constraint in terms of a single parameter, say t, substitute in f(x,y) to get a single variable function f(t), and hence put f'(t)=0, find maxima, and back-substitute to get maximum value. Here, x=1cos(t), y=1sin(t) can be used to easily obtain maximum value under constraint.

[@yizhang7027]

you can use the other two tangent points to find the minimum of f(x,y), right?

[@dinator12]

why is the maximum/minimum achieved where the contour lines touch? what if there was a higher value where they intersects? i mean, how can u be sure that the highest value achieved when the contour lines kisses?

[@dinator12]

only in these specific example the father u go from (0,0) the higher the function value is, what about other functions?

[@TheGaryAir]

The max value is achieved when the contour lines touch because the question is essentially asking you to find the greatest value for x^2y such that it is within the constraints. The highest value will be where the two graphs are tangent to one another because any greater would mean they're not intersecting and thus the function would not be within the constraint.

[@alexanderherbertkurz]

if they arent tangent but meet, then they intersect twice (if you assume that the lines are smooth enough (if that was what you worried about you were right, there are some conditions on the functions for Lagrange multipliers to work)) and if you move now the line so that it intersect not twice but only once you get a bigger (or smaller, depending on the direction you move) value, ie the original one was not the one you were looking for

[@joluju2375]

Just pour water into the 3D view, and it becomes obvious.

[@sathvikswaminathan7933]

but wouldn't this be the case only if the function is increasing with x and y?

[@albertres]

Clear as crystal. Thanks.

[@yavarjn2055]

How this video was made? Which tool permits to project a curve on a surface and at the same time to write beside it?

[@SolvingOptimizationProblems]

How many ways to solve constrained optimization problems? Anyone knows?

[@dimitrab6485]

Not to undermine the amazing work, but perhaps it would be even more helpful if the videos were explicitly numbered, especially for someone looking up subjects covered in older videos. Sure there are ways to figure out the order, but it would be quicker if all video titles included the part number. Thanks!

[@alexanderherbertkurz]

kzbin.info/aero/PLSQl0a2vh4HC5feHa6Rc5c0wbRTx56nF7

[@dimitrab6485]

Thanks!

[@RodrigoCastroAngelo]

You can also check the program on khan academy where, besides the lecture videos, they have lots of exercises: www.khanacademy.org/math/multivariable-calculus

[@renata8938]

Can I ask what program you used to draw the 3d graph? It is really good.

[@rikthecuber]

Finally a comment that is less than a year old!

[@Drganguli]

Nice video on Optimization

[@fatemehentezari9779]

Ohhh thank you. Your videos on optimization and linear algebra has made life much easier for me :) Thank you so much. Could we ask you to make some videos about optimization with inequality constraints? The way you explain the math, makes math easy and enjoyable.

[@shahzebansari6585]

You can make inequality into equality by introducing a variable called fictitious variable. Like x + y < 10 can be converted to x + y + w = 10, here w is fictitious variable.

[@sduio89]

Is it a convex or a non convex probelem due to the constraint?

[@sammao8478]

I love your video! Can I ask a question please? At 1:30 image, it seems that there are 6 local min/max points all together. The two in addition to the 4 you mentioned are at (0, 1) and (0, -1) with function value f(x, y) equals to zero. Now the question is weather can Lagrangian multiplier be zero? Thank you if you can help me to clarify this.

[@hipstertrudy3658]

I believe the most common context this is used in is economics, where resources cannot be negative, so youre probably right that there is 6 technically but for pragmatics hes just focused on the positive values

[@PBPotter]

This problem contains an implied (hidden) constraint that isn’t addressed in the video. Attending to this constraint will get you the other two optimization points. If you look at the original constraint x^2+y^2=1, that implies that 1 - y^2 >=0. So all the optimization point have to fall in that region. All the points found in the video do. But we also need to check the boundary of that region, y^2=1, or y= +/-1. Putting into the original f(x,y) equation and optimizing that will give you the two other optimization points that are missing in this video.

[@bradleycollings8176]

anyone know what graphing utility is used here?

[@luffyorama]

I think he used same codes like his channel (3Blue1Brown). He wrote some python codes for that.

[@jarednitta1934]

It kinda looks like the grapher app that comes on macs.

[@nestoreleuteriopaivabendo5415]

What about how he writes so smoothly on the screen...? Boy, there are plenty of people that want to write like this!

[@yavarjn2055]

How do you project a circle on a surface in python?

[@seungjunlee00]

can I ask just one question:) If I want to know the ​difference of Lagrange multipliers between Transcendental function and Calculus, what Khan Academy videos should i watch? Thank you in advance :)

[@mathematicalsmorgasbord762]

Hey SeungJun, not quite sure I understand your question. Do you mean you want to know how lagrange multipliers are different when you're working with transcendental functions as opposed to polynomials?

[@amjeda.a.7415]

Great explanation Thank you

[@surrealboy7453]

What software was used?

[@MuammarElKhatib]

Excellent video. Thanks :).

[@Dwika34]

men what is this software to graph ?

[@kunwar2010]

Grant Sanderson for the president!

[@jadoonengr79]

Can anyone give an idea how I can create such 3D graph. There are plenty out there but I need to replicate the exact same thing as in this video.

[@tsungiriraimunhuwamambo4053]

This is so informative

[@krishnapoduru8490]

I don't understand. Why does the unit circle doesn't intersect the x^2y graph instead lie along it?

[@LodrakFaust]

That was just a projection of the intersection of the unit circle (cylinder) on the 3d graph of the x^2y formel.

[@justkarl2922]

I don't really get the point here, why you build up these heavy weapons such as gradients and lagrange-multipliers. I can easily solve this problem with single variable calculus just by rewriting the constrain x^2 + y^2 =1 into x^2 = 1 - y^2 and substitute that in the original function f(x,y) =(x^2)*y so that f(y) = (1 - y^2)*y = -y^3 + y. Now I can optimize this with single vari. calc. et voilà!

[@iatbo0503]

justkarl it’s because the example here is very simple, almost trivial in a sense. Many expressions don’t have closed form solutions, and direct substitution is often very hard due to domain constraints, etc. Indeed, complex methods don’t make sense for this particular problem, but it lays groundwork for understanding more complex problems.

[@kimiyak5255]

Who is this teacher and how do I reach him? his explanations are really good , I want to learn more from him.

[@WhoTheHeIlCares]

He has a YT channel called 3blue1brown

[@kimiyak5255]

n1er dude thank you!

[@ArunKumar-yb2jn]

Hey, are you the same guy from 3BlueBrown?

[@saurabhsingh-ow7ue]

thank you sir

[@aishi99]

thank you so much!

[@youyoudz4346]

Some one help me I want to use and solve this in Matlab

[@yazan2776]

Is this differential or multivariable calculus?

[@justinward3679]

Yazan Multivariable

[@CederVeltman-ul8by]

His voice sounds exactly like 3b1b. Is it him?

[@AvinashSingh-bk8kg]

Hat's off 🎩

[@Postermaestro]

Commenting to spread on the tubes!

[@y0n1n1x]

Amazing

[@taraspokalchuk7256]

to good to be true

[@YashGupta-sf1kn]

there's something on the red circle which made me wipe my screen

[@g3452sgp]

Who is teaching?

[@tsungiriraimunhuwamambo4053]

People who disliked this need serious help 😂

[@proximaism]

I knew it's Sandersons.

[@jasspreet_kaurr]

👍👍

[@flaguser4196]

the guy sounds like 3blue1brown