Examples for optimization subject to inequality constraints, Kuhn-Tucker

Two examples for optimization subject to inequality constraints, Kuhn-Tucker necessary conditions, sufficient conditions, constraint qualification

Errata: At 17:32, (6/5, 8/5) is the only candidate point; (6/5, -8/5) does not satisfy the equation 4-2\lambda_1 y=0. At 46:55, (0,0) is not a candidate point, since it contradicts y larger than 2. At 50:56, it should be +26, not -26.

[TheFringless]

Watching mathematics for economists' video as a control engineering student for tomorrow's optimization exam. Life is so strange :D

[АсельМаженова-що]

Currently took Optimization Theory course, and your tutorial is the only thing that helped me to understand the material, thank you!

[snehalll]

You have no idea how much this helped. You are a SAVIOUR. Thank you.

[Veev_]

This is so helpful, I couldn't get a better explanation for my kuhn tucker conditions

[sylvatshi.]

at 47:02, you got y =0, but the constraint was for y> 2 therefore (0, 0 ) shouldn't be a candidate point

[katlegolebelwane]

Speechless 🙊! You saved me, I didn't understand this concept. I watched so many YouTube videos. Then I stumbled upon this one. Thanks a gazillion.

[beda]

Thank you for your service. I subscribed. Greetings from Colombia.

[paynehunter]

At the first problem, isn't y=-8/5 wrong?If you substite negative y and lambda1=5/4 in the second lagrange equation(dL/dy), it won't give us 0.The second lagrange equation results in 0 only for y=8/5.Doesn't this mean that (6/5, -8/5) is not a critical point?Maybe I'm wrong, but I'm curious.The video is very helpful by the way thanks a lot.

[byhtan]

I can't thank you enough :) simple yet concise!

[MichelleHernandez-fp]

Minute 47: How can (0, 0) be a candidate point if Y is supposed to be strictly greater than two?

[wassimmani]

How do you know the function is concave in 23rd minute? Shouldn't we use bordered hessian matrix?

[samueldodo]

Thank you . You 'save a soul'.

[gijskalender]

Amazing vid! few questions, is it right that you made 2 small mistakes in the end or maybe im wrong. Just for my personal clarification. In the last case of your second example isn't y=0 in contradiction with the condition that y>2? And when your simplifying the langrange in order to check the sufficiently, isn't it +26 instead of -26? Well, it were just some doubts, really great and useful vid!

[nahidfarazi]

should not Lambda >=0 at the beginning?

[siddharthdhillon]

the lagrange conditions are wrong? dont you think

[aidatopic]

Excellent video, thank you so much for posting it!

[pandupambudi]

why it's minus with constraint and not plus (Lagrangean)? i mean why not but I know the result will be the same with 4 cases conditions but they just opposite

[enyasandoval]

what happened in 40:40? i used the general formula and got something waaaay different

[Nostalgia-futuro]

Hello, if we have 3 constants, but only two variables (x1, x2), do we add 3rd lamda

[orestisexarchos]

What happens if they are linearly dependent vectors for all values of x, y or how are the constraint qualifications formed if we only have one constraint since we get points and not vectors??