Coupling methods for continuum models with molecular models are developed. Two methods are studied here: an overlapping domain decomposition method, which has overlapping domain, and an edge-to-edge decomposition method, which has an interface between two models. These two methods enforce the compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or t...

We consider the local convergence properties of the class of augmented Lagrangian methods for solving nonlinear programming problems whose global convergence properties are analyzed by Conn et al. (1993a). In these methods, linear constraints are treated separately from more general constraints. These latter constraints are combined with the objective function in an augmented Lagrangian while t...

We present a unified approach in analyzing Uzawa iterative algorithms for saddle point problems. We study the classical Uzawa method, the augmented Lagrangian method, and two versions of inexact Uzawa algorithms. The target application is the Stokes system, but other saddle point systems, e.g., arising from mortar methods or Lagrange multipliers methods, can benefit from our study. We prove con...

Abstract In this paper, we provide a new insight to the two-phase signal segmentation problem. We propose an augmented Lagrangian variational model based on Chan–Vese’s original one. Using both energy methods and PDE methods, show, in one-dimensional case, that set of minimizers proposed functional contains only binary functions it coincides with This fact allows us obtain two important feature...