As I know the l_2 norm (or l_1 or infinity) operation on a linear transform is a convex function? isn’t that true or the problem is having them (nonlinear functions) in the constraints. In that case can I reformulate my problem as an unconstraint problem with a negative regularization parameter (\lambda) as
$$\text{minimize} |Aw|_\infty + \lambda |Aw|_2$$
Thanks