Primal-dual regularized SQP and SQCQP type methods for convex programming and their complexity analysis

This paper presents and studies the iteration-complexity of two new inexact variants of Rockafellar’s proximal method of multipliers (PMM) for solving convex programming (CP) problems with a fi nite number of functional inequality constraints. In contrast to the first variant which solves convex quadratic programming (QP) subproblems at every iteration, the second one solves convex constrained … Read more

A note on Fejér-monotone sequences in product spaces and its applications to the dual convergence of augmented Lagrangian methods

In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that theirs limit points are dual … Read more