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.

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:

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...

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

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 ...