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...

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

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 ...

In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The proposed IAL framework requires solving the augmented Lagrangian (AL) subproblem at each iteration less accurately than most of the exist...

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-no...

We deal with a generalization of the proximal-point method and the closely related Tikhonov regularization method for convex optimization problems. The prime motivation behind this is the well-known connection between the classical proximal-point and augmented Lagrangian methods, and the emergence of modified augmented Lagrangian methods in recent years. Our discussion includes a formal proof o...

This paper presents a method based on nonlinear programming for short term scheduling of hydro power system. The proposed algorithm is based on the solution of an augmented lagrangian function of the scheduling problem using conjugate gradient method. The water transportation delay between cascaded reservoirs is considered. Results concerning this method are compared with those achieved from su...

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton li...