R help - Jul 2012 - finding the values to minimize sum of functions

Hi fellow R users,

I am desperately hoping there is an easy way to do this in R.

Say I have three functions:

f(x) = x^2
f(y) = 2y^2
f(z) = 3z^2

constrained such that x+y+z=c (let c=1 for simplicity).

I want to find the values of x,y,z that will minimize f(x) + f(y) + f(z).

I know I can use the optim function when there is only one function, but
don't know how to set it up when there are three.

I would also like to apply this to higher dimensions (i.e. for more than
three functions) if possible.

Thank you for all your help!

--
Kind regards,

Linh Tran, MPH

Hi Linh,

Here is an approach:

f <- function(v) {
  v <- v/sum(v)
  (v[1]^2) + (2 * v[2]^2) + (3*v[3]^2)
}

(res <- optim(c(.6, .3, .1), f))

res$par/sum(res$par)

This is a downright lazy way to implement the constraint.  The main
idea is to combine all three functions into one function that takes a
vector of parameters (v, in this case).

Cheers,

Josh

On Thu, Jul 19, 2012 at 10:24 AM, Linh Tran <Tranlm at berkeley.edu>
wrote:
> Hi fellow R users,
>
> I am desperately hoping there is an easy way to do this in R.
>
> Say I have three functions:
>
> f(x) = x^2
> f(y) = 2y^2
> f(z) = 3z^2
>
> constrained such that x+y+z=c (let c=1 for simplicity).
>
> I want to find the values of x,y,z that will minimize f(x) + f(y) + f(z).
>
> I know I can use the optim function when there is only one function, but
> don't know how to set it up when there are three.
>
> I would also like to apply this to higher dimensions (i.e. for more than
> three functions) if possible.
>
> Thank you for all your help!
>
> --
> Kind regards,
>
> Linh Tran, MPH
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.


-- 
Joshua Wiley
Ph.D. Student, Health Psychology
Programmer Analyst II, Statistical Consulting Group
University of California, Los Angeles
https://joshuawiley.com/

On Thu, Jul 19, 2012 at 10:24:17AM -0700, Linh Tran
wrote:
> Hi fellow R users,
> 
> I am desperately hoping there is an easy way to do this in R.
> 
> Say I have three functions:
> 
> f(x) = x^2
> f(y) = 2y^2
> f(z) = 3z^2
> 
> constrained such that x+y+z=c (let c=1 for simplicity).
> 
> I want to find the values of x,y,z that will minimize f(x) + f(y) + f(z).
Hi.

If the constraint is linear as in this case, it is possible
to eliminate one of the varibles. Instead of minimizing

  x^2 + 2y^2 + 3z^2

under the constraint x+y+z = c, minimize, for example

  x^2 + 2y^2 + 3(c - x - y)^2

with no constraint.

Hope this helps.

Petr Savicky.