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On weighted linear least-squares problems related to interior methods for convex quadratic programming
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-6252-7815
2001 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 23, no 1, 42-56 p.Article in journal (Refereed) Published
Abstract [en]

It is known that the norm of the solution to a weighted linear least-squares problem is uniformly bounded for the set of diagonally dominant symmetric positive definite weigh matrices. This result is extended to weigh matrices that are nonnegative linear combinations of symmetric positive semidefinite matrices. Further, results are given concerning the strong connection between the boundedness of weighted projection onto a subspace and the projection onto its complementary subspace using the inverse weigh matrix. In particular, explicit bounds are given for the Euclidean norm of the projections. These results are applied to the Newton equations arising in a primal-dual interior method for convex quadratic programming and boundedness is shown for the corresponding projection operator.

Place, publisher, year, edition, pages
2001. Vol. 23, no 1, 42-56 p.
Keyword [en]
unconstrained linear least-squares problem, weighted least-squares, problem, quadratic programming, interior method, scaled projections, point methods, stability, systems, pseudoinverses, matrices, factorizations, algorithms, equations
URN: urn:nbn:se:kth:diva-20898ISI: 000170613100003OAI: diva2:339595
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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