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...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

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 ...

In this section, we derive in detail the closed form solution of problem (12) for binary pairwise factors (Sect. 4.1). Recall that the marginal polytope M(G a) is given by:

An augmented Lagrangian iterative scheme for mixed nite element methods is proposed and analyzed in an abstract framework. This framework is put in a general and computationally eecient fashion, and is based on the idea of iteratively penalizing the mixed nite element scheme. It is shown that the scheme has geometrical convergence.

We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata. In this paper, we propose several iterative schemes based on the alternating direction method of multipliers for solving the nonnegative inverse problem. We also extend our sch...

Appropriate selection of the penalty parameter is crucial to obtaining good performance from the Alternating Direction Method of Multipliers (ADMM). While analytic results for optimal selection of this parameter are very limited, there is a heuristic method that appears to be relatively successful in a number of different problems. The contribution of this paper is to demonstrate that their is ...