Maximum a posteriori (MAP) inference is one of the fundamental inference tasks in graphical models. MAP inference is in general NP-hard, making approximate methods of interest for many problems. One successful class of approximate inference algorithms is based on linear programming (LP) relaxations. The augmented Lagrangian method can be used to overcome a lack of strict convexity in LP relaxat...

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a mi...

A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the n×n submatrix residing in the (1,1)block of the (n+m)×(n+m) augmented matrix that would generate non-expansive iterations in R. The classic multiplier me...

For a given iterate generated by the augmented Lagrangian or the Lagrangian relaxation based method, we derive estimates for the distance to the primal solution of the underlying optimization problem. The estimates are obtained using some recent contributions to the sensitivity theory, under appropriate first or second order sufficient optimality conditions. The given estimates hold in situatio...

A novel relaxation labeling (RL) method is presented based on Augmented Lagrangian multipliers and the graded Hoppeld neural network (ALH). In this method, an RL problem is converted into a constrained optimization problem and solved by using the augmented Lagrangian and Hoppeld techniques. The ALH method yields results comparable to the best of the existing RL algorithms in terms of the optimi...

We define a primal-dual algorithm model (SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exact augmented Lagrangian function and the use ...

An augmented Lagrangian method with second-order update is developed, and its relationship to the sequential quadratic programming method is described. The rate of convergence proof depends on a second-order sufficient optimality condition, which is shown to be satisfied for a class of nonlinear optimal control problems of tracking type. Numerical examples are included which demonstrate the glo...

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εk-global minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an ε-global minimizer of the original problem is proved. The subproblems are solved...

In this paper we study optimal control problems of the uid ow governed by the Navier-Stokes equations. Two control problems are formulated in the case of the driven cavity and ow through a channel with sudden expansion and solved successfully using a numerical method based on the augmented Lagrangian method. Existence and rst order optimality condition of the optimal control are established. A ...