dc.contributor.author Chua, Chek Beng. dc.date.accessioned 2009-07-28T01:16:03Z dc.date.available 2009-07-28T01:16:03Z dc.date.copyright 2007 en_US dc.date.issued 2007 dc.identifier.citation Chua, C. B. (2007). The primal-dual second-order cone approximations algorithm for symmetric cone programming. Foundations of computational mathematics, (7)3, 273-302. en_US dc.identifier.issn 1615-3383 en_US dc.identifier.uri http://hdl.handle.net/10220/4707 dc.description.abstract Given any open convex cone K, a logarithmically homogeneous, self-concordant barrier for K and any positive real number r < 1, we associate, with each direction x 2 K, a second-order cone ˆKr(x) containing K. We show that K is the interior of the intersection of the second-order cones ˆKr(x), as x ranges over all directions in K. Using these second-order cones as approximations to cones of symmetric, positive definite matrices, we develop a new polynomial-time primal-dual interior-point algorithm for semidefinite programming. The algorithm is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras. en_US dc.format.extent 27 p. en_US dc.language.iso en en_US dc.relation.ispartofseries Foundations of Computational Mathematics. en_US dc.rights Foundations of computational mathematics @ copyright 2000 Springer Verlag. The jourmal's websites is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/106038/ en_US dc.subject DRNTU::Science::Mathematics::Applied mathematics::Optimization dc.title The primal-dual second-order cone approximations algorithm for symmetric cone programming en_US dc.type Journal Article dc.contributor.school School of Physical and Mathematical Sciences en_US dc.identifier.doi http://dx.doi.org/10.1007/s10208-004-0149-7 dc.description.version Accepted version en_US
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