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Constrained Extrema and Lagrange Multipliers

  1. Mar 25, 2015 #1
    Suppose I have a function f(x,y) I would like to optimize, subject to constraint g(x,y)=0.

    Let H=f+λg,

    The extrema occurs at (x,y) which satisfy
    Hy=0
    Hx=0
    g(x,y)=0

    Suppose the solutions are (a,b) and (c,d).

    If f(a,b)=f(c,d) , how do I determine whether they are maxima or minima?
     
  2. jcsd
  3. Mar 25, 2015 #2

    mathman

    User Avatar
    Science Advisor

    One way is brute force. Evaluate the function slightly away from the test point.
     
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