[R] finding the values to minimize sum of functions

Petr Savicky savicky at cs.cas.cz
Thu Jul 19 21:28:08 CEST 2012

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).


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.

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