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International Conference on Applied Mathematics and Sustainable Development -Special track within SCET2012

Xi'an,China,2012.5.27-5.302012

ISBN: 978-1-61896-023-8 srp

Paperback 630pp Pub. Date: May 2012

Category: Physics & Mathematics

Price: $80

Title: Preconditioning Indefinite Systems in Interior-Point Methods for quadratic optimization
Source: International Conference on Applied Mathematics and Sustainable Development -Special track within SCET2012 (pp 275-277)
Author(s):
Abstract: Abstract—A new class of preconditioners is proposed for the iterative
solution of symmetric indefinite systems arising from interior-
point methods. The use of logarithmic barriers in interior
point methods causes unavoidable ill-conditioning of linear systems
and, hence, iterative methods fail to provide sufficient accuracy
unless appropriately preconditioned. Now we introduce two
types of preconditioners which use some form of incomplete Cholesky
factorization for indefinite systems. For convex optimization
problems all the eigenvalues of this matrix are strictly positive.
Meanwhile, we apply the new regularization techniques for
symmetric indefinite systems to improve the stability of our iterative
approach. Numerical results are given for a set of public
domain large linearly constrained convex quadratic programming
problems with sizes reaching tens of thousands of variables.
The analysis of these results provides the potential advantages of
our approach when applied to the solution of very large quadratic
problems.
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