An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems

Augmented Lagrangian and Total Variation Methods for Recovering Discontinuous Coeecients from Elliptic Equations

Estimation of coeecients of partial diierential equations is ill-posed. Output-least-squares method is often used in practice. Convergence of the commonly used minimization algorithms for the inverse problem is often very slow. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled linear algebraic system, which can be solved eeciently. Total variation techniques ...

A Numerical Study of an Augmented Lagrangian Method for the Estimation of Parameters in Elliptic Systems

Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization

We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its wellestablished ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic outputleast-squares formul...

Finite Element Solutions of Cantilever and Fixed Actuator Beams Using Augmented Lagrangian Methods

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...

Augmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...