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

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- Oct 3rd 2010, 08:09 PMstrawlionLagrangian multiplier
A quick question... when do you add the lamba times constraint and when do you subtract? Or does it matter?

- Oct 4th 2010, 01:31 AMmr fantastic
- Oct 4th 2010, 02:51 AMHallsofIvy
In fact, I have always thought of it as "gradient of object function

**equals**$\displaystyle \lambda$ times gradient of constraint function" rather than adding or subtracting.

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