Permutating a matrix in a convex form

Permutating a matrix in a convex form

I am at the basis of convex optimization and I made a constraint written
in the following form:
$XAY\le M$
where:
$A\in R^{3,4}$ given, $a_{ij} \in \{0,1\}\quad \forall i,j$
$X\in R^{3,3}$ variable
$Y\in R^{4,4}$ variable
$M\in R^{3,4}$ variable
In this case $X$ and $Y$ are my "permutation matrices", in the sense that
they are composed by 0s or 1s with the sum of each column(and row) is
equal to 1
Thank you very much in advance