# Maximizing a set of functions

1. Mar 2, 2007

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) $$f_1(x)$$
(2) $$f_2(x,W,H)$$
(3) $$f_3(x,W,H)$$

that form a function:

$$F(x,W,H) = f_1 + f_2 + f_3$$

How would I maximize $$F(x,W,H)$$.

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. Mar 2, 2007

### Dick

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. Mar 3, 2007

Are f1,f2,f3 convex?

4. Mar 3, 2007

### HallsofIvy

ARE W and H variables or are they constants? I see no reason to use "Lagrange multipliers" because you have no constraints.

5. Mar 3, 2007

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. Mar 3, 2007

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. Mar 3, 2007