for all x ∈ IR, λ ∈ IR, μ ∈ IR +. PHR-based Augmented Lagrangian methods for solving (1) are based on the iterative (approximate) minimization of Lρ with respect to x ∈ Ω, followed by the updating of the penalty parameter ρ and the Lagrange multipliers approximations λ and μ. The most popular practical Augmented Lagrangian method gave rise to the Lancelot package [24, 25, 26]. Lancelot does not...

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...

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 ...

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...

A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. We discuss in this paper augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discu...