On Thu, May 17, 2012 at 06:14:37PM -0400, Nathan Stephens wrote:
> I have a very simple maximization problem where I'm solving for the vector
> x:
>
> objective function:
> w'x = value to maximize
>
> box constraints (for all elements of w):
> low < x < high
>
> equality constraint:
> sum(x) = 1
Hi.
As Peter Dalgaard suggested, lpSolve may be used. If "low" may contain
negative values, then it is important to note that lpSolve assumes
all variables nonnegative. So, a transformation is needed, for example
x = low + y and solve for y. The following is one approach.
library(lpSolve)
n <- 8
w <- 1:n
low <- rep(-1, times=n)
high <- rep(1, times=n)
crit <- w
mat <- rbind(diag(n), 1)
rhs <- c(high - low, 1 - sum(low))
dir <- c(rep("<=", times=n), "==")
out <- lp("max", objective.in=crit, const.mat=mat, const.dir=dir,
const.rhs=rhs)
x <- low + out$solution
round(x, digits=15)
[1] -1 -1 -1 0 1 1 1 1
Hope this helps.
Petr Savicky.
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