Minimization of quadratic forms using the Drazin-inverse solution

We analyse the problem of constrained minimization of the real quadratic functional , subject to the inconsistent system of linear equations , where is a positive definite or positive semidefinite matrix. Both cases are analysed separately, and respective relationships have been established between...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 62; no. 2; pp. 252 - 266
Main Authors Stanimirović, Predrag S., Pappas, Dimitrios, Miljković, Sladjana
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.02.2014
Taylor & Francis Ltd
Subjects
Algebra
Algorithms
constrained optimization
Constraints
Drazin inverse
Minimization
Moore-Penrose inverse
Optimization
outer inverse
Quadratic forms
quadratic functional
Queuing theory
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Summary:We analyse the problem of constrained minimization of the real quadratic functional , subject to the inconsistent system of linear equations , where is a positive definite or positive semidefinite matrix. Both cases are analysed separately, and respective relationships have been established between the solution of the original problem and the Drazin-inverse solution of the equation . In the special case when is a positive definite and , we show that the solution of the problem can be represented as a particular -inverse solution.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2013.771639