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Maximizing a set of functions

  • Thread starter FrogPad
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  • #1
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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.
 

Answers and Replies

  • #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.
 
  • #3
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Are f1,f2,f3 convex?
 
  • #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.
 
  • #5
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Are f1,f2,f3 convex?
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.
 
  • #6
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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.
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.
 
  • #7
809
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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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