On 9/7/07, Phil Xiang <[EMAIL PROTECTED]> wrote:
> I need to optimize a multivariate function f(w, x, y, z, ...) under an
> absolute value constraint. For instance:
>
> min { (2x+y) (w-z) }
>
> under the constraint:
>
> |w| + |x| + |y| + |z| = 1.0 .
>
> Is there any R function that does this? Thank you for your help!
I think that the minimum value of the function
f(x) := -2*x*(1-x), with 0 <= x <= 1
is also the minimum value of the objective function of your problem
(but correct me if I am wrong). Thus,
x y w z
-0.5 0 0 -0.5
-0.5 0 0.1 -0.4
-0.5 0 0.3 -0.2
0.5 0 -0.5 0
-0.5 0 0.5 0
0.5 0 -0.4 0.1
0.5 0 -0.2 0.3
0.5 0 0 0.5
are all solutions for your problem.
Paul
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