Thread: Lagrange Multiplier

Was going through a question that's already been done in the class. When I compared my results with my lecturer's I spotted I had for some critical points, whereas my lecturer only had non-zero values for it.

Is always a non-zero value? I can't be sure as I have terrible notes.

I think that if lambda is 0 then your solution happens to lie on a stationary point of the (unconstrained) objective function, and so that particular constraint has no effect. Do you agree?

Spoiler:

suppose we're maximising f(x) subject to g(x) the lagrangian is

at the optimal point:



so if lamda =0 then



and the unconstrained objective function is at a stationary point.

if there was more than one constraint, then the interpretation is a bit messier, of course.