Result: Model problems for the multigrid optimization of systems governed by differential equations

Title:
Model problems for the multigrid optimization of systems governed by differential equations
Authors:
LEWIS, Robert Michael, NASH, Stephen G
Source:
SIAM journal on scientific computing (Print). 26(6):1811-1837
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2005.
Publication Year:
2005
Physical Description:
print, 29 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations aux dérivées partielles, problèmes aux valeurs initiales et problèmes aux valeurs limites dépendant du temps, Partial differential equations, initial value problems and time-dependant initial-boundary value problems, Equations aux dérivées partielles, problèmes aux valeurs limites, Partial differential equations, boundary value problems, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Analyse numérique, Numerical analysis, Análisis numérico, Calcul scientifique, Scientific computation, Computación científica, Décomposition domaine, Domain decomposition, Descomposición dominio, Equation différentielle, Differential equation, Ecuación diferencial, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Méthode décomposition, Decomposition method, Método descomposición, Méthode optimisation, Optimization method, Método optimización, Problème valeur initiale, Initial value problem, Problema valor inicial, Problème valeur limite, Boundary value problem, Problema valor limite, Programmation mathématique, Mathematical programming, Programación matemática, Programmation non linéaire, Non linear programming, Programación no lineal, Système différentiel, Differential system, Systema diferencial, Algorithme multigrille, Optimisation non linéaire, Problème optimisation, 65M55, 65N55, multigrid methods, optimization of systems governed by differential equations 65K05
Document Type:
Academic journal Article
File Description:
text
Language:
English
ISSN:
1064-8275
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17225975
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17225975
Database:
PASCAL Archive

Further Information

We discuss a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems appear in many applications and are of a different nature than systems of equations. Our approach uses an optimization-based multigrid algorithm in which the multigrid algorithm relies explicitly on nonlinear optimization models as subproblems on coarser grids. Our goal is not to argue for a particular optimization-based multigrid algorithm, but instead to demonstrate how multigrid can be used to accelerate nonlinear programming algorithms. Furthermore, using several model problems we give evidence (both theoretical and numerical) that the optimization setting is well suited to multigrid algorithms. Some of the model problems show that the optimization problem may be more amenable to multigrid than the governing differential equation. In addition, we relate the multigrid approach to more traditional optimization methods as further justification for the use of an optimization-based multigrid algorithm.