Paper Info
Title
On an Inequality of C. Sundberg: A Computational Investigation via Nonlinear Programming.
Abstract
The main goal of this article is to discuss a numerical method for finding the best constant in a Sobolev type inequality considered by C. Sundberg, and originating from Operator Theory. To simplify the investigation, we reduce the original problem to a parameterized family of simpler problems, which are constrained optimization problems from Calculus of Variations. To decouple the various differential operators and nonlinearities occurring in these constrained optimization problems, we introduce an appropriate augmented Lagrangian functional, whose saddle-points provide the solutions we are looking for. To compute these saddle-points, we use an Uzawa–Douglas–Rachford algorithm, which, combined with a finite difference approximation, leads to numerical results suggesting that the best constant is about five times smaller than the constant provided by an analytical investigation.
Year
DOI
Venue
2013
10.1007/s10957-013-0275-y
J. Optimization Theory and Applications
Keywords
Field
DocType
Nonlinear variational problem, Augmented Lagrangian method, Alternating direction method of multipliers
Mathematical optimization,Finite difference,Mathematical analysis,Parametric family,Calculus of variations,Sobolev space,Nonlinear programming,Augmented Lagrangian method,Lagrangian relaxation,Operator theory,Mathematics
Journal
Volume
Issue
ISSN
158
3
1573-2878
Citations 
PageRank 
References 
1
0.35
5
Authors
2
Name
Order
Citations
PageRank
Roland Glowinski118850.44
Annalisa Quaini2499.50