We introduce a filter mechanism to force convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows fo...

This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

Abstract In this paper we will present a review of recent advances in the application augmented Lagrange multiplier method as general approach for generating multiplier-free stabilised methods. The Lagrangian consists standard by penalty term, penalising constraint equations, and is well known basis iterative algorithms constrained optimisation problems. Its use stabilisation methods computatio...

We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a lo...

A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two di erent ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computa...

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 constraint. In this paper, we develop two FOMs constrained convex programs, where the constraint set is represented by affine equations and smooth nonlinear inequalities. Both are based on classical augmented Lagrangian func...

In this paper, the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real-valued function are established via a generalized augmented Lagrangian and corresponding generalized augmented Lagrangian problems, in which no convexity is imposed on the augmenting function. These results further imply a zero duality gap property between th...

This report considers the solution of estimation problems based on the maximum likelihood principle when a xed number of equality constraints are imposed on the problem. Consistency and the asymptotic distribution of the parameter estimates as n ! 1, where n is the number of observations, are discussed, and it is shown that a suitably scaled limiting multiplier vector is known. It is suggested ...