0

I'm currently self studying calculus of variations and stumbled upon something called a Lagrange multiplier, used in solving isoperimetric problems and the like. Not knowing what they are I backtrack and found this wikipedia article.

Ok, so I see how they are use full in combination with calculus of variation, however the problem described by wikipedia can be solved by substituting a parametric representation of the constraint into the function and find extrema using normal calculus.

What are the limitations of this method (the substitution one) and why are Lagrange multipliers used instead? What additional classes of problem can they be applied to apart from the mentioned ones?

Michal
  • 298
  • 1
    The examples on wikipedia aren't particularly useful for the LM because there are only two variables involved and as such you just have to make a substitution and it's an one variable calculus problem. Look around on MSE for examples with three variables or more. See this recent example. – Git Gud Mar 02 '14 at 23:32
  • Plus Lagrange multipliers are incredibly easy to calculate, as long as you have no trouble finding solutions to simultaneous equations. – George1811 Mar 02 '14 at 23:35

0 Answers0