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...

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...

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...

A generally nonconvex optimization problem with equality constraints is studied. The problem is introduced as an “inf sup” of a generalized augmented Lagrangian function. A dual problem is defined as the “sup inf’ of the same generalized augmented Lagrangian. Sufftcient conditions are derived for constructing the augmented Lagrangian function such that the extremal values of the primal and dual...

In constrained optimisation, the augmented Lagrangian method is considered as one of the most effective and efficient methods. This paper studies the behaviour of augmented Lagrangian function (ALF) in the solution space and then proposes an improved augmented Lagrangian method. We have shown that our proposed method can overcome some of the drawbacks of the conventional augmented Lagrangian me...

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pu...

This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

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...

We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a lo...