A multiplier method with a class of penalty functions for convex programming

We consider a class of augmented Lagrangian methods for solving convex programming problems with inequality constraints. This class involves a family of penalty functions and specific values of parameters p, q, ỹ ∈ R and c > 0. The penalty family includes the classical modified barrier and the exponential function. The associated proximal method for solving the dual problem is also considered. Convergence results are shown, specifically we prove that any limit point of the primal and the dual sequence generated by the algorithms are optimal solutions of the primal and dual problem respectively.