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Maximizing a set of functions

  1. Mar 2, 2007 #1
    I am working on a paper for a class, and I've come to somewhat of a block. I'll keep the question general.

    If I have three non-linear real valued functions,

    (1) [tex] f_1(x) [/tex]
    (2) [tex] f_2(x,W,H) [/tex]
    (3) [tex] f_3(x,W,H) [/tex]

    that form a function:

    [tex] F(x,W,H) = f_1 + f_2 + f_3 [/tex]

    How would I maximize [tex] F(x,W,H) [/tex].

    Lagrange multipliers are ringing a bell... but before I get too invested in an idea, I would like the proper road to travel down. So If someone could point me in the right direction that would be awesome.
     
  2. jcsd
  3. Mar 2, 2007 #2

    Dick

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    You're just minimizing the sum of the functions. Take partial derivatives of the sum wrt to x, W and H and set them all to zero.
     
  4. Mar 3, 2007 #3
    Are f1,f2,f3 convex?
     
  5. Mar 3, 2007 #4

    HallsofIvy

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    ARE W and H variables or are they constants? I see no reason to use "Lagrange multipliers" because you have no constraints.
     
  6. Mar 3, 2007 #5
    I am not actually sure. They are mixed with a lot of different terms (sinh, cosh, ...), so it is hard (for me at least) to get an idea of what they look like.
     
  7. Mar 3, 2007 #6
    I've recently found out that W corresponds to some constants in the functions, so I can no longer vary it.

    So I will have the following:

    f(x,W) = const = f1(x)+f2(x,H)+f3(x,H)

    x and W both represent the length of a device. I am trying to find lengths that that maximize f(x,W), which actually represent a current.
     
  8. Mar 3, 2007 #7
    Thanks for the help everyone.

    The expressions were too complicated to take derivatives of and solve in such a way (too time consuming at least). I ended up writing a brute force algorithm to try all possible values (from a pool of "intelligent" guesses) to maximize the function.

    I appreciate the help.
     
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