A local saddle point for the hyperbolic augmented Lagrangian function

In this paper, we study the hyperbolic augmented Lagrangian function, which is based on the hyperbolic penalty function. We ensure the existence of a local saddle point for the hyperbolic augmented Lagrangian function in nonconvex constrained optimization problems by considering the classical second-order sufficiency conditions. Finally, we present some computational illustrations of the theory proposed in this work.