Abstract

In this work, Solodov–Svaiter’s hybrid projection-proximal and extragradient-proximal methods [16,17] are used to derive two algorithms to find a Karush–Kuhn–Tucker pair of a convex programming problem. These algorithms are variations of the proximal augmented Lagrangian. As a main feature, both algorithms allow for a fixed relative accuracy of the solution of the unconstrained subproblems. We also show that the convergence is Q-linear under strong second order assumptions. Preliminary computational experiments are also presented.