[R] Cardinality constraint

[Patrick Burns]

To solve the problem you have in general, you will need
something more powerful than 'constrOptim'.  This is called
a mixed integer problem, and arises in several fields including
financial portfolio optimization.

If you really only have 3 variables, then there are only 3
combinations of 2 variables.  So just solve the problem with
each set and pick the best one.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

Neuro LeSuperHéros wrote:

>Hello,
>
>How do I implement a cardinality constraint with constrOptim?
>
>I want to minimize (least square) a%*%x = 4
>subject to
>x1<2
>x2<1
>x3<4
>count(x1, x2, x3)= 2 (cardinality constraint)
>
>Is there a way to specify binary integer variables with constrOptim?
>
>Here's my code so far:
>
>a <-matrix(1:3,1,3)
>fr <-  function(x) {
>(a%*%x-4)^2
>     }
>constrOptim(c(1,0.5,3),fr,grad=NULL,ui=-diag(3), ci=c(-2,-1,-4))
>
>I need the optimization to give me one variable that is zero to satisfy the 
>maximum cardinality of 2.
>
>Thanks
>
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