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...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

Abstract We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling framework for variety of applications. study stationarity regularity concepts, propose flexible augmented Lagrangian scheme. provide theoretical characte...

We suggest a new approach to solve class of degenerate Hamilton–Jacobi equations without any assumptions on the emptiness Aubry set. It is based characterization maximal subsolution by means Fenchel–Rockafellar duality. This enables us use augmented Lagrangian methods as alternatives commonly used for numerical approximation solution, finite difference or optimal control interpretation solution.

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 develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...

Since the late 1990s, the interest in augmented Lagrangian methods has been revived, and several models with smooth penalty functions for programs with inequality constraints have been proposed, tested and used in a variety of applications. Global convergence results for some of these methods have been published. Here we present a local convergence analysis for a large class of smooth augmented...