Constrained optimization introduction

See a simple example of a constrained optimization problem and start getting a feel for how to think about it. This introduces the topic of Lagrange multipliers.

[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

[preetkanwalsingh]

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

[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)

[robertwilsoniii]

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

[alijavadyfar]

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 !

[huynjinful]

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

[AlleyCat]

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

[Prism]

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

[SohamChakraborty]

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.

[TheDroidMate]

When the two most appreciated educators team up. 😍

[jamesgoodman]

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

[Tomahawk]

mathematics when explained this way is actually much more interesting.

[ericbischoff]

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 :-)

[fatemehentezari]

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.

[shkittle]

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

[yizhang]

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

[yavarjn]

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

[sathvikswaminathan]

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

[jadoonengr]

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.

[SolvingOptimizationProblems]

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