Asymptotical good behavior on inequalities with completely approximate K–T concept

We characterize a wide class of regular convex functionals that are asymptotically well behaved on a convex set given by (infinite) inequalities, namely, those restricted functions whose stationary sequences (bounded or not) are minimizing ones. After showing the equivalence with the Kuhn–Tucker type stationarity, we prove that the class of such functions remains unchanged when the Kuhn–Tucker system is completely relaxed. This allows us to proceed for enlarging the scope of convergence of certain penalty (exterior as well as interior) methods including a new exterior penalization for infinite inequalities.