Lagrange multipliers method

Question

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

Answer 1

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

Answer 2

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.