Augmented Lagrangian functions for constrained optimization problems

In this paper, in order to obtain some existence results about solutions of the augmented Lagrangian problem for a constrained problem in which the objective function and constraint functions are noncoercive, we construct a new augmented Lagrangian function by using an auxiliary function. We establish a zero duality gap result and a sufficient condition of an exact penalization representation for the constrained problem without the coercive or level‐bounded assumption on the objective function and constraint functions. By assuming that the sequence of multipliers is bounded, we obtain the existence of a global minimum and an asymptotically minimizing sequence for the constrained optimization problem.