[R] Cardinality constraint

[Neuro LeSuperHéros]

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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