Open AccessBook
Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics
Reads0
Chats0
TLDR
In this article, an augmented Lagrangian method for the solution of variational problems is proposed. But this method is not suitable for continuous media and their mathematical modeling, such as viscoplasticity and elastoviscasticity.Abstract:
1. Some continuous media and their mathematical modeling 2. Variational formulations of the mechanical problems 3. Augmented Lagrangian methods for the solution of variational problems 4. Viscoplasticity and elastoviscoplasticity in small strains 5. Limit load analysis 6. Two-dimensional flow of incompressible viscoplastic fluids 7. Finite elasticity 8. Large displacement calculations of flexible rods References Index.read more
Citations
More filters
Journal ArticleDOI
A proximal multiplier method for separable convex minimization
TL;DR: In this paper, an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure was proposed, which unifies the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM), and Auslender and Teeboulle(EPDM).
Journal ArticleDOI
Explicit algorithms to solve a class of state constrained parabolic optimal control problems
TL;DR: In this article, an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative is considered.
Journal ArticleDOI
On the augmented Lagrangian approach to Signorini elastic contact problem
TL;DR: The Signorini problem is transformed into a saddle point problem of some augmented Lagrangian functional and then discretized by finite element methods to obtain optimal error estimates for general smooth domains which are not necessarily convex.
Journal ArticleDOI
New decomposition methods for solving variational inequality problems
Deren Han,Wenyu Sun +1 more
TL;DR: In this paper, a decomposition method based on the Lagrange and augmented Lagrange mappings of the variational inequality problems is proposed, which solves the original problem via solving a series of small-scale problems, which may be much easier to solve than the original problems.
Journal ArticleDOI
Solving a non-smooth eigenvalue problem using operator-splitting methods
TL;DR: The Peaceman–Rachford scheme turns out to be superior to the Marchuk–Yanenko scheme in terms of accuracy and computational efficiency.
Related Papers (5)
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
A dual algorithm for the solution of nonlinear variational problems via finite element approximation
Daniel Gabay,Bertrand Mercier +1 more