The hyperbolic augmented Lagrangian algorithm (HALA) is introduced in the area of continuous optimization for solving nonlinear programming problems. Under mild assumptions, such as: convexity, Slater’s qualification and differentiability, the convergence
of the proposed algorithm is proved. We also study the duality theory for the case of the hyperbolic augmented Lagrangian function. Finally, in order to illustrate the algorithm, we present some computational experiments.