Finding Maxima, Minima, and Saddle Points with Lagrange Multipliers

In summary, the speaker is having trouble finding the actual values for the multipliers and points and is seeking a method to determine whether the collected points are maxima, minima, or saddle points. They have looked through many books and found the 'Bordered Hessian' method, but the criteria is not clearly described. They are asking for help or guidance on where to find a clear explanation.
  • #1
ythamsten
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I'm currently having some trouble, after the procedure of finding the actual values for the multipliers and the points, but how come can I figure out whether which points that I've collected are maxima, minima or just saddle ones. I've taken a look on lots of books, but I can't seem to find something that helps me out with a method that I can apply in general. The closest I reached of something useful was called the 'Bordered Hessian', which was fairly similar to usual optimization, but where I was reading, the criteria was described in kind of a fuzzy way. Can someone help me? Or at least indicate where I can find this in a clear way? Thanks!
 
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  • #2
This should help you
 
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Likes ythamsten
  • #3
It surely did zoki85! Thanks a lot.
 

Related to Finding Maxima, Minima, and Saddle Points with Lagrange Multipliers

1. What are Lagrange multipliers?

Lagrange multipliers are a mathematical technique used to find the maximum or minimum value of a function subject to certain constraints. They are named after mathematician Joseph-Louis Lagrange, who first described the method in the 18th century.

2. How do Lagrange multipliers work?

Lagrange multipliers work by introducing a new variable, called a multiplier, to the original function. This multiplier is then used to create a new function, which can be solved using traditional calculus methods to find the maximum or minimum value. The constraints are taken into account by setting the gradient of this new function equal to the gradient of the original function multiplied by the multiplier.

3. When should Lagrange multipliers be used?

Lagrange multipliers are best used when optimizing a function subject to one or more constraints. They are particularly useful in cases where the constraints are difficult to incorporate into the original function or when the function has multiple variables.

4. What are the advantages of using Lagrange multipliers?

One of the main advantages of using Lagrange multipliers is their ability to handle complex constraints. They also provide a systematic approach to solving optimization problems, making it easier to find the maximum or minimum value of a function. Additionally, they can be used to solve both single-variable and multi-variable problems.

5. Are there any limitations to using Lagrange multipliers?

One limitation of Lagrange multipliers is that they can only be used for continuous functions. They also rely on the assumption that the constraints are independent, which may not always be the case. Additionally, they can be computationally intensive for problems with multiple constraints or variables.

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