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 customized Douglas---Rachford splitting algorithm for separable convex minimization with linear constraints
TL;DR: It is shown that the primal application of DRSM in combination with an appropriate decomposition can yield an efficient structure-exploiting algorithm for the model under consideration, whose subproblems could be easier than those of ADMM.
Posted Content
On the Convergence Rate of Multi-Block ADMM
TL;DR: Convergence and convergence rate results for the standard ADMM applied to solve N-block (N 3) convex minimization problem are presented, under the condition that one of these functions is convex (not necessarily strongly convex) and the other N 1 functions are strong convex.
Journal ArticleDOI
Alternating direction splittings for block angular parallel optimization
TL;DR: Numerical results for large-scale multicommodity flow problems are presented to demonstrate the effectiveness of these decomposition algorithmims on the Thinking Machines CM-5 parallel supercomputer relative to the widely-used serial optimization package MINOS 5.4.
Journal ArticleDOI
An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications
Zdenÿek Dostal,Tomaÿs Kozubek +1 more
TL;DR: The MPGP algorithm can be used for minimization of a strictly convex quadratic function subject to separable convex constraints and its optimality is demonstrated on the solution of a problem of two cantilever beams in mutual contact with Tresca friction discretized by almost twelve millions nodal variables.
Journal ArticleDOI
On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems
Gerard Awanou,Ming-Jun Lai +1 more
TL;DR: The purpose of this paper is to give a rate of convergence of a variant of the augmented Lagrangian algorithm in the nonsymmetric case and illustrate the performance of this algorithm with numerical simulations of the lid-driven cavity flow problem for the 2D Navier-Stokes equations.
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