Augmented Lagrangian Methods
Applications to the Numerical Solution of Boundary-Value Problems
Published on 1. April 2000
339 pages
978-0-08-087536-1 (ISBN)
Description
The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.
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M. Fortin | R. Glowinski
Augmented Lagrangian Methods: Volume 15
Applications to the Numerical Solution of Boundary-Value Problems
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04/2000
North-Holland
€107.70
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Content
- Front Cover
- Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems
- Copyright Page
- Table of Contents
- Chapter 1. Augmented Lagrangian Methods in Quadratic Programming
- 1. Principles of the Method
- 2. A First Algorithm for Saddle-Point Calculation
- 3. Variable Step-Length Algorithms . Conjugate Gradient Method
- 4. On Certain Variants of the Methods of Section 2 : Introduction of a Relaxation Parameter
- Method of Arrow-Hurwicz
- 5. Miscellaneous Remarks and Discussion
- Chapter 2. Application to the Stokes and Navier-Stokes Equations
- 1. Introduction
- 2. Discretisation of the Stokes Problern
- 3. Algorithms and Discussion of Results
- 4. Navier - Stokes Equations, Steady-State Nonlinear Case
- 5. Variants and Approximations of the Basic Algorithm of Section 4
- 6. Navier-Stokes Equations. Time-Dependent Case
- 7. General Discussion on Chapter II
- Chapter 3. On Decomposition-Coordination Methods Using an Augmented Lagrangian
- 1. Introduction
- 2. Investigation of Problem (P) and of the Saddle-Points of L and L
- 3. Description of the Algorithms
- 4. Convergence of ALG1
- 5. Convergence of ALG2
- 6. Application to Some Nonlinear Problems
- 7. Application to Nonlinear Programming Problems
- 8. General Discussion on Chapter III
- Chapter 4. Numerical Solution of Mildly Nonlinear Problems by Augmented Lagrangian Methods
- 1. Introduction
- 2. A Class of Mildly Nonlinear Elliptic Problems
- 3. Augmented Lagrangian and Decomposition of the Problem (2.5),(2.6)
- 4. Algorithms for Solution of the Approximate Problem (2.13) . Discussion
- 5. Numerical Experiments
- 6. Some Remarks on Hybrid Methods
- 7. General Discussion on Chapter IV
- Chapter 5. Application to the Solution of Strongly Nonlinear Second-Order Boundary Value Problems
- 1. Introduction
- 2. General Framework of the Problems in Chapter V
- 3. A Class of Nonlinear Dirichlet Problems
- 4. A Magneto-Static Problem
- 5. Calculation of Subsonic and Transonic Potential Flows
- 6. Further applications
- 7. Discussion on Chapter V
- Chapter 6. Application of Algorithm ALG2 to a two Dimensional elastoplasticity Problem
- Introduction
- 1. The Continuous Problem
- 2. The Problem ( P)
- 3. Approximation by Finite Elements
- 4. Application of Algorithm ALG2
- 5. Convergence of Algorithm ALG2
- 6. Numerical Application
- 7. Discussion
- Chapter 7. Application to the Numerical Solution of the two Dimensional Flow of Incompressible Viscoplastic Fluids
- 1. General Notes. Synopsis
- 2. Formulation of Bingham Flows Using the Velocity and the Pressure
- 3. Formulation of Bingham Flows using A Stream Function
- 4. Approximation of the Steady-State Problem
- 5. Approximation of the Evolution Problem (3.7)
- 6. Solution of (4.1) (5.2) by Augmented Lagrangian Methods
- 7. Numerical Experiments
- Chapter 8. Application to the Solution of Finite Nonlinear Elasticity Problems
- 1. General Notes . Synopsis
- 2. Decomposition of Variational Problems. Associated Algorithms.
- 3. Applications in Finite Nonlinear Elasticity . (I) Large- Displacement Calculation of the Equilibrium Positions of Inextensible, Flexible pipelines
- 4. Applications in Finite Nonlinear Elasticity. (II) Two-Dimensional Calculations Involving Large Displacements and Large Strains for Incompressiblem Materials of Mooney-Rivlin Type
- 5. Some Remarks on the Application of the Algorithms of Section 2 to the Solution of Eigenvalue and Eigenvector Problems
- Chapter 9. Applications of the Method of Multipliers to Variational Inequalities
- 1. Introduction
- 2. The Proximal Point Algorithm
- 3. Variational Inequalities in Duality
- 4. The Method of Multipliers for Variational Inequalities
- 5. Decomposition by Multipliers : (I) Alternating Direction Methods
- 6. Decomposition by Multipliers : (II) Projection Methods
- 7. General Discussion
- References
