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Full Record Details
DOI
10.5286/raltr.2008017
Persistent URL
http://purl.org/net/epubs/work/43759
Record Status
Checked
Record Id
43759
Title
A Bramble-Pasciak-like method with applications in optimization
Contributors
HS Dollar (STFC Rutherford Appleton Lab.)
,
NIM Gould (STFC Rutherford Appleton Lab.)
,
M Stoll (Oxford U. Computing Lab)
,
AJ Wathen (Oxford U. Computing Lab)
Abstract
Saddle-point systems arise in many applications areas, in fact in any situation where extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is an example coming form partial differential equations and in the area of Optimization such problems are ubiquitous. In this manuscript we show how new approaches for the solution of saddle-point systems arising in Optimization can be derived from the Bramble-Pasciak Conjugate Gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of Preconditioned Conjugate Gradients in non-standard inner products and demonstrate how these can be understood through more standard machinery. We show connections to Constraint Preconditioning and give the results of numerical computations on a number of standard Optimization test examples.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
conjugate gradient methods
,
Krylov subspaces
,
linear systems
,
preconditioning
,
saddle-point problems
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2008-017. STFC, 2008.
dgswRAL2008017.pdf
2008
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