Augmented Lagrangian algorithms are very popular tools for solving nonlinear programming problems. At each outer iteration of these methods a simpler optimization problem is solved, for which efficient algorithms can be used, especially when the problems are large. The most famous Augmented Lagrangian algorithm for minimization with inequality constraints is known as Powell-Hestenes-Rockafellar...

We consider the variational inequality problem formed by a general set-valued maximal monotone operator and a possibly unbounded “box” in Rn , and study its solution by proximal methods whose distance regularizations are coercive over the box. We prove convergence for a class of double regularizations generalizing a previously-proposed class of Auslender et al. Using these results, we derive a ...

We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem...

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...

Inverse problems related to the estimation of coeecients of partial diierential equations are illposed. Practical applications often use the t-to-data output-least-square's method to recover the coeecients. In this work, we develop parallel nonoverlapping domain decomposition algorithms to estimate the diiusion coeecient associated with elliptic diierential equations. In order to realize the do...

This thesis deals with the development of numerical methods for solving nonconvex optimisation problems by means of decomposition and continuation techniques. We first introduce a novel decomposition algorithm based on alternating gradient projections and augmented Lagrangian relaxations. A proof of local convergence is given under standard assumptions. The effect of different stopping criteria...

ABSTRACT We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in different ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a sequence of subproblems; in eac...

In this paper we present an accelerated Augmented Lagrangian Method for the solution of constrained convex optimization problems in the Basis Pursuit De-Noising (BPDN) form. The technique relies on on Augmented Lagrangian Methods (ALMs), particularly the Alternating Direction Method of Multipliers (ADMM). Here, we present an application of the Constrained Split Augmented Lagrangian Shrinkage Al...