# Lagrangian multiplier

• October 3rd 2010, 08:09 PM
strawlion
Lagrangian multiplier
A quick question... when do you add the lamba times constraint and when do you subtract? Or does it matter?
• October 4th 2010, 01:31 AM
mr fantastic
Quote:

Originally Posted by strawlion
A quick question... when do you add the lamba times constraint and when do you subtract? Or does it matter?

It does not matter.
• October 4th 2010, 02:51 AM
HallsofIvy
In fact, I have always thought of it as "gradient of object function equals $\lambda$ times gradient of constraint function" rather than adding or subtracting.

$\nabla F= \lambda\nabla G$ is, of course, the same as $\nabla F- \lambda \nable G= \nabla(F- \lambda G)= 0$ but $\nabla(F+ \lambda G)= 0$ involves only changing the sign on $\lambda$ which is unknown, anyway.