  In this paper we propose an Approximate Weak stationarity ($AW$-stationarity)
concept designed to deal with {\em Mathematical Programs with Cardinality
Constraints} (MPCaC), and we proved that it is a legitimate optimality
condition independently of any constraint qualification. Such a sequential
optimality condition improves weaker stationarity conditions, presented in a
previous work. Many research on sequential optimality conditions has been
addressed for nonlinear constrained optimization in the last few years, some
works in the context of MPCC and, as far as we know, no sequential optimality
condition has been proposed for MPCaC problems. We also establish some
relationships between our $AW$-stationarity and other usual sequential
optimality conditions, such as AKKT, CAKKT and PAKKT. We point out that,
despite the computational appeal of the sequential optimality conditions, in
this work we are not concerned with algorithmic consequences. Our aim is purely
to discuss theoretical aspects of such conditions for MPCaC problems.
