# finding the values to minimize sum of functions

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## 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: finding the values to minimize sum of functions

 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 <[hidden email]> 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 > > ______________________________________________ > [hidden email] 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/______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.