Replying to a control engineering student's comment on a economist's video for mathematics to ignore tomorrow's computer science exam on optimization. Life's strange.
this is so natural because this kuhn-tucker method and some other optimizing stuffs are used samely in both fields. economics and finance are came from natural science in some degrees.
Given that all optimization and equation solving happens using computers with these algorithms built in anyway, it's redundant to teach the math anymore to anyone but those who want to specialize in optimization techniques. An intuition and a set of guidelines on when to use what is more than enough
Watching mathematics for economists' video as a chemical engineering student for my thesis subject which I don't understand anything, and watching english videos because there's not videos in spanish. :'D
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.
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!
is that because it is either slack or binding. for slack, it doesn't satisfy the equality condition in constraint, hence the lambda will be 0 anyway whereas for binding, it satisfies the equality condition and the gradient of the maximized function at solution will be a linear combination of all constraints gradient and each scalar will be in effect, hence lambda be >0. so in short, it is either lambda = 0 or > 0
You channel is really instructive. I also went ahead to download your lecture notes but found only your lecture note on linear algebra. Can you kindly include that of optimization? Thank you.
Hi, thanks for the tutorial. It's really great! I just want to comment at 38:00 you write 3x - λ1 = 0, However the second equation should be 3y - λ1 = 0 or λ1 = 3y. This makes the calculation on the next substitution to be cubic formula because dL/dx = 4x+3y-λ1x = 0 to be 4x+3y-3xy = 0. Thanks and have a great day!
why it's minus with constraint and not plus (Lagrangean)? i mean 3x+4y-lambda1*(const1)-lambda2*(const2)? why not 3x+4y+lambda1*(const1)+lambda2*(const2). but I know the result will be the same with 4 cases conditions but they just opposite
at 17:15 , there shouldn't be two candidate points because (6/5, -8/5) will imply a negative lambda from equation 2 , right? so there should be only one point (6/5,8/5) ... please respond to my query.
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??
There are many possible ways to write optimization problems subject to inequality constraints, and it can get confusing at times. I like to write things this way: max f(x) s.t. g(x) = b, with Lagrangian L = f + lambda (g-b), g-b >= 0, lambda >= 0. Why did I change minus to plus in L? min f s.t. g >= b is equivalent to max -f s.t. -g = 0 in the max-case, and in the min-case, this derivative is -lambda = 0), but increasing b by one unit leads to a lambda-increase in the max-objective function, and a lambda-decrease in the min-objective function. Another reason to write things this way is the standard formulation of the Lagrange multiplier theorem: grad f = lambda grad g, that is, grad f - lambda grad g = 0. Of course you can do it differently, and in both cases write L = f + lambda (g-b), then lambda = 0 in the min-case. I guess this is what you found in a book.
Your solution is wrong, because the point (2,2) is not in the feasible region, at (2,2) the inequality constraints do not satisfied. The correct answer is the point (1, sqrt(3)) for max, and (1,-sqrt(3)) for min.
So sad to see what economics has become. Economics is about human behaviour. Keynesianism and trying to make economics a scientific field is why economics today is pointless. Very sad to see.
Thank you for this comment. You have put forward quite an interesting idea. In some capacity, I agree with you. However, the Kuhn Tucker technique on optimization is not especially useful in the cases you mention (i.e. explaining human behavior and economic trends). It is, however, very useful in quantifiable cases of profit optimization, efficiency optimization. It can be very useful to shipping companies, energy providers and charities. Please let me know what you think.
@@TheInavsayo if it is very useful to the REAL WORLD then why not teach that. I need examples. Start applying theory with examples. Majority of theory is bs.
@@qeoo6578 that is general for linear optimization problems and provably so. it is way more general than whatever economics you are into. so calling it bs is extremely dumb
It is synonymous. although there's a controversy about that, you can still understand the context so what is the matter. Also you said sir, so South asia? I don't see any brits here complaining about the word usage, so why should we, speaker of english as second language, complain about such trivial matter?
