Examples for optimization subject to inequality constraints, Kuhn-Tucker

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  • Опубликовано: 23 окт 2024

Комментарии • 87

  • @TheFringless
    @TheFringless 6 лет назад +100

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

    • @pawan-td6ff
      @pawan-td6ff 5 лет назад +20

      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.

    • @wooinchoi8161
      @wooinchoi8161 5 лет назад +6

      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.

    • @RexGalilae
      @RexGalilae 5 лет назад +2

      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

    • @suyash.01
      @suyash.01 4 года назад

      watching this video as a computer science student. strange?

    • @alchem1s7
      @alchem1s7 4 года назад +1

      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

  • @АсельМаженова-щ2о
    @АсельМаженова-щ2о 2 года назад +13

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

  • @snehalll15
    @snehalll15 7 лет назад +12

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

  • @Veev_
    @Veev_ 4 года назад +7

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

  • @sylvatshi.6808
    @sylvatshi.6808 6 лет назад +13

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

    • @mathematicsforeconomists7739
      @mathematicsforeconomists7739  6 лет назад +2

      Thanks for catching. Check the errata in the video description, there were a few more that slipped through my net.

  • @katlegolebelwane3318
    @katlegolebelwane3318 3 года назад +1

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

  • @beda5107
    @beda5107 5 лет назад +2

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

  • @paynehunter
    @paynehunter 7 лет назад +5

    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.

  • @byhtan001
    @byhtan001 6 лет назад +10

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

  • @MichelleHernandez-f9p
    @MichelleHernandez-f9p 7 месяцев назад

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

  • @wassimmani952
    @wassimmani952 10 месяцев назад

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

  • @samueldodo7187
    @samueldodo7187 4 года назад +2

    Thank you . You 'save a soul'.

  • @vinayakkhanna47
    @vinayakkhanna47 5 лет назад +3

    Extremely helpful video. Thanks a lot

  • @gijskalender1328
    @gijskalender1328 7 лет назад +5

    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!

    • @mathematicsforeconomists7739
      @mathematicsforeconomists7739  7 лет назад +9

      Thanks for catching these. Indeed, at 46:55, (0,0) is not a candidate point, since it clearly contradicts y>2. At 50:56, it should be +26, not -26.

  • @nahidfarazi8382
    @nahidfarazi8382 5 лет назад +6

    should not Lambda >=0 at the beginning?

    • @andeslam7370
      @andeslam7370 4 года назад

      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

  • @siddharthdhillon1311
    @siddharthdhillon1311 5 лет назад +10

    the lagrange conditions are wrong? dont you think

  • @aidatopic4796
    @aidatopic4796 3 года назад

    Excellent video, thank you so much for posting it!

  • @pandupambudi5690
    @pandupambudi5690 4 года назад

    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

  • @enyasandoval1224
    @enyasandoval1224 5 лет назад +1

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

  • @trangvuthikieu3226
    @trangvuthikieu3226 2 года назад

    Thank you for posting

  • @magedrefat1658
    @magedrefat1658 4 года назад +1

    Amazing, thank you very much.

  • @aaronbelakhoua5497
    @aaronbelakhoua5497 6 лет назад +1

    Great video, very grateful!

  • @Nostalgia-futuro
    @Nostalgia-futuro 4 года назад

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

  • @orestisexarchos2190
    @orestisexarchos2190 7 лет назад

    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??

  • @oyololafeyisayo5468
    @oyololafeyisayo5468 3 года назад

    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.

  • @joeyye1
    @joeyye1 7 лет назад

    Thanks for the video. By any chance,can you upload your working?

  • @nazimnariman6645
    @nazimnariman6645 3 года назад

    Great lecture......thank you so much.

  • @HiPh0Plover1
    @HiPh0Plover1 7 лет назад +1

    can you explain why in some books we find that lambdas must be negative in the max case and positive in the min case ?

    • @mathematicsforeconomists7739
      @mathematicsforeconomists7739  7 лет назад +10

      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.

    • @HiPh0Plover1
      @HiPh0Plover1 7 лет назад

      thanks for full reply

  • @marlonbrade9004
    @marlonbrade9004 4 года назад

    What if you got a case where there is no multiplier is positive? what is the approach?

  • @yasasp5781
    @yasasp5781 7 лет назад +1

    @9:50 how did the x attached to -2*lambda1 disappear? was this a mistake?

    • @profitab
      @profitab 7 лет назад

      putting the value of x=1.

  • @manasvisharma1304
    @manasvisharma1304 7 лет назад +4

    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.

  • @ΧαρηςΦλωρος-ν1ι
    @ΧαρηςΦλωρος-ν1ι 5 лет назад

    In 9:33 he writes 3- 4/sqt3 + λ2 instead of 3- (4/sqt3)*x + λ2

  • @upomarahman6654
    @upomarahman6654 3 года назад

    Thank you 😊

  • @marina816
    @marina816 4 года назад +1

    the lagrangian should be + lambda

  • @ambreenfirdous3732
    @ambreenfirdous3732 3 года назад

    Very good video

  • @joescerbo6125
    @joescerbo6125 3 года назад

    Thanks

  • @satriapriambada8599
    @satriapriambada8599 4 года назад

    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!

  • @zdzislawnajmrocki4739
    @zdzislawnajmrocki4739 4 года назад

    Sir, Thanks Great job

  • @manqobantshakala3821
    @manqobantshakala3821 2 года назад

    The best vid by far

  • @alperenonal6527
    @alperenonal6527 Год назад

    ty so much , pdf pls :)

  • @tomisthlm
    @tomisthlm 7 лет назад

    at 13:21 you forgot the 2 in the denominator.

  • @josearturoarroyonavarrete3958
    @josearturoarroyonavarrete3958 5 лет назад

    T H A N K Y O U!!

  • @aysunozturan1428
    @aysunozturan1428 2 года назад

    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.

  • @mohamedhachami3279
    @mohamedhachami3279 2 года назад

    2puissanse 2 + 2puissance 2 > 4 !!!!

    • @mathematicsforeconomists7739
      @mathematicsforeconomists7739  Год назад

      You jumped in the vid. The solution (2,2) is from the second problem, and you put it into the constraint of the first problem.

  • @georgekiros5229
    @georgekiros5229 2 года назад +1

    are mad or............?

  • @royalexchc
    @royalexchc 5 лет назад +1

    I don't speak english xD :"c

  • @DiegoRodriguez-ns9br
    @DiegoRodriguez-ns9br 5 лет назад

    tamal

  • @shakir4429
    @shakir4429 2 года назад

    0q

  • @qeoo6578
    @qeoo6578 5 лет назад +6

    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.

    • @TheInavsayo
      @TheInavsayo 5 лет назад +2

      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.

    • @qeoo6578
      @qeoo6578 5 лет назад +1

      @@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.

    • @rings4433
      @rings4433 5 лет назад +2

      @@qeoo6578 Perhaps a career in applied economics is what you're looking for.

    • @98danielray
      @98danielray 5 лет назад

      @@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

    • @VainCape
      @VainCape 4 года назад +1

      Sad indeed. Economics has been bastardized into a subfield of math. And then people complain economics has become stale and uncreative

  • @37-nguyenthanhtung91
    @37-nguyenthanhtung91 4 года назад

    u r wrong

  • @merc340sr
    @merc340sr 6 лет назад +2

    Dear sir, I realize your mother tongue is not English but please say ''REGARDLESS", or ''IRRESPECTIVE", NOT "IRREGARDLESS". Thank you.

    • @nitahandastya9262
      @nitahandastya9262 4 года назад +1

      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?

  • @kamrulhassan7157
    @kamrulhassan7157 Месяц назад

    💚💚💚💚💚💚💚💚💚 thanks a lot sir

  • @nazlieronat
    @nazlieronat 4 года назад

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