❖ LaGrange Multipliers - Finding Maximum or Minimum Values ❖
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users cite it as a worked walkthrough of the Lagrange multiplier method, mostly when a question shows someone struggling to follow a constrained optimization example.
Recommended by 1 people across 1 different months, 2012 to 2018.
What it is
A roughly 10 minute tutorial by Patrick J on using Lagrange multipliers to find maxima and minima of a function under a constraint. It covers the general procedure of setting up and solving the partial derivative equations, then works through a word problem example.
What people said
Recommends William Chang · 2014-03 · Mathematics Stack Exchange · on “Minima and maxima of multivariable equations”
In general, to find the maxima and minima of a given function, you can set the first derivatives, $f_h$, $f_r$ equal to 0 and then check endpoints/places where the function is undefined. Lagrange multipliers are usually applied with a constraint, not to find global maxima and minima of a function. But for this specific function, we can see that the function does not have an upper bound or lower bound. We see that $f(r,h)$ approaches infinity or negative infinity as r and h go to 0. So intuitively, if we let r and h be arbitrarily smalls number, we see that the function trails off to infinity. If we let r be an arbitrarily small negative number and h be an arbitrarily large positive value, we
Cites Raynos · 2012-03 · Mathematics Stack Exchange · on “Lagrange Multiplier optimization, not getting correct answer.”
can you please explain how you got that? I was following this video and got D=0 which is wrong: [this video] I know that in the first step you differentiated that function with respect to x then y for the 2nd equation but how do you know though which answers to take that are within boundary? like i dont get how to got all sorts of cos and sins in there
Cites Kong · 2017-09 · Mathematics Stack Exchange · on “Prefix Code with Minimum Expected Length - Lagrange Multiplier”
I was reading the section on finding optimal codes through the lagrange multiplier and saw this expression at page 16 of [LINK] The goal is to minimize $ \sum p_i l_i $ subject to $ \sum D^{-li} \le 1$ The formulation using langrange multipliers thus becomes $ \min( J = \sum p_i l_i + \lambda(\sum D^{-li})) $ The first step is to differentiate the equation wrt $l_i$ and $\lambda$ and set it to zero. $ \frac{dJ}{dl_i} = p_i - \lambda D^{-li}ln \ D = 0 \\ D^{-li} = \frac{p_i}{\lambda \ ln \ D} \\ \frac{dJ}{d\lambda} = \sum D^{-li} = 0 $ But then my next steps would not be the same as the slides. This is what I would do. $ \sum D^{-li} = 0 \\ \sum \frac{p_i}{\lambda \ ln \ D} = 0 \\ \frac{1}{\l
Cites J.Doe · 2018-06 · Mathematics Stack Exchange · on “Lagrange multiplier plus or minus”
I am working through different tutorials about Lagrange multiplier and came upon a problem. It seems like that there's different ways to solve. You have a given equation $f(x,y)$ and a constraint $g(x,y)$. A few tutorials then start to set the derivatives respect to $x$ and $y$ of $\lambda\,g(x,y)$ and $f(x,y)$ equal to each other and start solving for variables: $$f(x,y)= \lambda\,g(x,y) \tag{1}$$ or use a form of $$F(x,y,\lambda)=f(x,y) - \lambda \,g(x,y)\tag2$$ which is basically the same since you can subtract the right hand side of $(1)$ and derive $(2)$. Other tutorials use a form of $$F(x,y,\lambda)= f(x,y) + \lambda\,g(x,y)\tag3$$ So the main difference is the minus and the plus in t