This book offers a comprehensive presentation of some of the most successful and popular
domain decomposition preconditioners for finite and spectral element approximations of …

Augmented Lagrangian methods with general lower-level constraints are considered in the
present research. These methods are useful when efficient algorithms exist for solving …

These notes serve as an introduction to a subject of study in computational mathematics
referred to as domain decomposition methods. It concerns divide and conquer methods for …

Solving optimization problems in complex systems often requires the implementation of
advanced mathematical techniques. Quadratic programming (QP) is one technique that …

Abstract Two Augmented Lagrangian algorithms for solving KKT systems are introduced.
The algorithms differ in the way in which penalty parameters are updated. Possibly …

A new active set based algorithm is proposed that uses the conjugate gradient method to
explorethe face of the feasible region defined by the current iterate and the reduced gradient …

The finite element method (FEM) is a widely used numerical scheme to solve complex
partial differential equations stemming from science and engineering. Contact mechanics is …

In this paper we discuss a specialization of the augmented Lagrangian-type algorithm of
Conn, Gould, and Toint to the solution of strictly convex quadratic programming problems …

An efficient non-overlap** domain decomposition algorithm of the Neumann–Neumann
type for solving both coercive and semicoercive contact problems is presented. The …

Theoretical and experimental results concerning FETI based algorithms for contact problems
of elasticity are reviewed. A discretized model problem is first reduced by the duality theory …