TITLE: Lagrange multipliers method
QUESTION [5 upvotes]: I am currently doing some exercise on the Lagrange multipliers methods and have come upon some confusion. following my lectures notes is says:
$$L= f(x,y) + \lambda g(x,y) $$
and in some online examples it says:
$$L= f(x,y) - \lambda g(x,y) $$
where $f(x,y)$ is the function to be minimized/maximized and $g(x,y)$ is the constraint.
Which one is correct? many thanks

REPLY [5 votes]: actually it is same,because  we can  consider  signs as a alternatives  of maximize or minimize,so  you can use it without  any problem.
http://en.wikipedia.org/wiki/Lagrange_multiplier
maybe also  author's definition plays some role as well.so i think there is not  big difference between  $+$  sign ad $-$ sign in  this case
i found you  case
http://www1.maths.leeds.ac.uk/~cajones/math2640/notes4.pdf
please see this

REPLY [3 votes]: It doesn't matter which one you use, the $\lambda$ you get when solving the system of equations will just be the negative of the other method.