This is very easy:
You have |Ax| <= b
. This is equivalent to (as you yourself noted) to -b <= Ax <= b
.
So, you have additional inequality constraints: Ax <= b
and -Ax <= b
.
Thus you have over all AA = [ A ; -A ]
and bb = [b;b]
defining your abs-value constraints:
x = bintprog( f, AA, bb );