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Projector preconditioning for partially bound‐constrained quadratic optimization
Author(s) -
Domorádová Marta,
Dostál Zdeněk
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.555
Subject(s) - mathematics , discretization , conjugate gradient method , projection (relational algebra) , boundary (topology) , rate of convergence , convergence (economics) , quadratic equation , domain decomposition methods , variational inequality , augmented lagrangian method , quadratic programming , upper and lower bounds , projector , domain (mathematical analysis) , mathematical optimization , mathematical analysis , algorithm , finite element method , geometry , computer science , channel (broadcasting) , computer network , physics , economics , computer vision , thermodynamics , economic growth
Preconditioning by a conjugate projector is combined with the recently proposed modified proportioning with reduced gradient projection (MPRGP) algorithm for the solution of bound‐constrained quadratic programming problems. If applied to the partially bound‐constrained problems, such as those arising from the application of FETI‐based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is shown to have better bound on the rate of convergence than the original MPRGP algorithm. The performance of the algorithm is illustrated on the solution of a model boundary variational inequality. Copyright © 2007 John Wiley & Sons, Ltd.