Coupling general penalty schemes for convex programming with the steepest descent and the proximal point algorithm

We study the asymptotic behavior of the continuous flow generated by coupling the steepest descent method with a general class of penalty schemes for convex programming. We establish convergence of the trajectories towards primal optimal solutions, as well as convergence of some naturally associated dual paths. The results are extended to the sequences generated by an implicit discretization scheme which corresponds to the coupling of an inexact proximal point iteration with the penalty schemes.