A method for weighted projections to the positive definite cone

Handle URI:
http://hdl.handle.net/10754/597305
Title:
A method for weighted projections to the positive definite cone
Authors:
Valkonen, Tuomo
Abstract:
© 2014 Taylor & Francis. We study the numerical solution of the problem (Formula presented.) , where (Formula presented.) is a symmetric square matrix, and (Formula presented.) is a linear operator, such that (Formula presented.) is invertible. With (Formula presented.) the desired fractional duality gap, and (Formula presented.) the condition number of (Formula presented.) , we prove (Formula presented.) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints. We do not, however, require the numerically expensive scalings inherent in these methods to force fast convergence. For low-dimensional problems (Formula presented.), our numerical experiments indicate excellent performance and only a very slowly growing dependence of the convergence rate on (Formula presented.). While our algorithm requires somewhat more iterations than existing interior point methods, the iterations are cheaper. This gives better computational times.
Citation:
Valkonen T (2014) A method for weighted projections to the positive definite cone. Optimization 64: 2253–2275. Available: http://dx.doi.org/10.1080/02331934.2014.929680.
Publisher:
Informa UK Limited
Journal:
Optimization
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
24-Jun-2014
DOI:
10.1080/02331934.2014.929680
Type:
Article
ISSN:
0233-1934; 1029-4945
Sponsors:
This research was financially supported by the SFB research programme F32 ‘Mathematical Optimization and Applications in Biomedical Sciences’ of the Austrian Science Fund (FWF), and by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorValkonen, Tuomoen
dc.date.accessioned2016-02-25T12:30:17Zen
dc.date.available2016-02-25T12:30:17Zen
dc.date.issued2014-06-24en
dc.identifier.citationValkonen T (2014) A method for weighted projections to the positive definite cone. Optimization 64: 2253–2275. Available: http://dx.doi.org/10.1080/02331934.2014.929680.en
dc.identifier.issn0233-1934en
dc.identifier.issn1029-4945en
dc.identifier.doi10.1080/02331934.2014.929680en
dc.identifier.urihttp://hdl.handle.net/10754/597305en
dc.description.abstract© 2014 Taylor & Francis. We study the numerical solution of the problem (Formula presented.) , where (Formula presented.) is a symmetric square matrix, and (Formula presented.) is a linear operator, such that (Formula presented.) is invertible. With (Formula presented.) the desired fractional duality gap, and (Formula presented.) the condition number of (Formula presented.) , we prove (Formula presented.) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints. We do not, however, require the numerically expensive scalings inherent in these methods to force fast convergence. For low-dimensional problems (Formula presented.), our numerical experiments indicate excellent performance and only a very slowly growing dependence of the convergence rate on (Formula presented.). While our algorithm requires somewhat more iterations than existing interior point methods, the iterations are cheaper. This gives better computational times.en
dc.description.sponsorshipThis research was financially supported by the SFB research programme F32 ‘Mathematical Optimization and Applications in Biomedical Sciences’ of the Austrian Science Fund (FWF), and by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43.en
dc.publisherInforma UK Limiteden
dc.subjectinterior pointen
dc.subjectprojectionen
dc.subjectquadratic programming diffusion tensor imagingen
dc.subjectsemi-definiteen
dc.titleA method for weighted projections to the positive definite coneen
dc.typeArticleen
dc.identifier.journalOptimizationen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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