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Math Help - Lagrange Multiplier

  1. #1
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    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 \lambda = 0 for some critical points, whereas my lecturer only had non-zero values for it.

    Is \lambda always a non-zero value? I can't be sure as I have terrible notes.
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  2. #2
    MHF Contributor
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    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 L  = f(x) + \lambda g(x)

    at the optimal point:

    \dfrac{dL}{dx} = 0 = \dfrac{df}{dx} + \lambda

    so if lamda =0 then

    0 = \dfrac{df}{dx}

    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.

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