Augmented Lagrangian method (ALM) has been popularly used for solving constrained
optimization problems. Practically, subproblems for updating primal variables in the …

The augmented Lagrangian method (ALM) is one of the most useful methods for constrained
optimization. Its convergence has been well established under convexity assumptions or …

The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic
development of constrained optimization. In this paper, we mainly show that Nesterov's …

This paper considers a special class of convex programming (CP) problems whose feasible
regions consist of a simple compact convex set intersected with an affine manifold. We …

First-order methods have been studied for nonlinear constrained optimization within the
framework of the augmented Lagrangian method (ALM) or penalty method. We propose an …

In this paper we discuss a specialization of the augmented Lagrangian-type algorithm of
Conn, Gould, and Toint to the solution of strictly convex quadratic programming problems …

First-order methods (FOMs) have been popularly used for solving large-scale problems.
However, many existing works only consider unconstrained problems or those with simple …

In this paper we present a complete iteration complexity analysis of inexact first-order
Lagrangian and penalty methods for solving cone-constrained convex problems that have or …

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear
programming problems. At each outer iteration, a minimization subproblem with simple …

In this paper we study the worst-case complexity of an inexact augmented Lagrangian
method for nonconvex constrained problems. Assuming that the penalty parameters are …