A new notion of weighted centers for semidefinite programming.

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A new notion of weighted centers for semidefinite programming.

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dc.contributor.author Chua, Chek Beng.
dc.date.accessioned 2009-08-03T01:20:45Z
dc.date.available 2009-08-03T01:20:45Z
dc.date.copyright 2006
dc.date.issued 2009-08-03T01:20:45Z
dc.identifier.citation Chua, C. B. (2006). A new notion of weighted centers for semidefinite programming. SIAM Journal of Optimization, 16(4), 1092–1109.
dc.identifier.issn 1095-7189
dc.identifier.uri http://hdl.handle.net/10220/5988
dc.description.abstract The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties—(1) each choice of weights uniquely determines a pair of primal-dual weighted centers, and (2) the set of all primal-dual weighted centers completely fills up the relative interior of the primal-dual feasible region. This paper presents a new notion of weighted centers for semidefinite programming that possesses both uniqueness and completeness. Furthermore, it is shown that under strict complementarity, these weighted centers converge to weighted centers of optimal faces. Finally, this convergence result is applied to homogeneous cone programming, where the central paths defined by a certain class of optimal barriers for homogeneous cones are shown to converge to analytic centers of optimal faces in the presence of strictly complementary solutions.
dc.format.extent 18 p.
dc.language.iso en
dc.relation.ispartofseries SIAM Journal of Optimization.
dc.rights Siam Journal of Optimization @ copyright 2006 Society for Industrial and Applied Mathematics. The journal's website is located at http://www.siam.org/journals/siopt.php
dc.subject DRNTU::Science::Mathematics::Applied mathematics::Optimization.
dc.title A new notion of weighted centers for semidefinite programming.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.doi http://dx.doi.org/10.1137/040613378
dc.description.version Published version

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