A modified augmented Lagrangian method for a class of constrained problems

A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

An Augmented Lagrangian Method for a Class of Lmi-constrained Problems in Robust Control Theory

We present a new approach to a class of non-convex LMI-constrained problem in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with non-convex constraints related to rank conditions. We solve these problems using an extension of the augmented Lagrangian technique. The Lagrangia...

Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems

In this paper, we propose a smoothing augmented Lagrangian method for finding a stationary point of a nonsmooth and nonconvex optimization problem. We show that any accumulation point of the iteration sequence generated by the algorithm is a stationary point provided that the penalty parameters are bounded. Furthermore, we show that a weak version of the generalized Mangasarian Fromovitz constr...

A modified augmented Lagrangian method for a class of monotone variational inequalities

Abstract. The augmented Lagrangian method is an attractive approach for solving linearly constrained convex optimization problems (CCOP). The method is iterative and the task in each iteration is to solve a (convex optimization) sub-problem whose dimension is equal to the number of variables. For large problems, solving such a sub-problem can be still very expensive. In this paper, we propose a...

On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces