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# The primal-dual second-order cone approximations algorithm for symmetric cone programming.

 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 dc.date.issued 2009-07-28T01:16:03Z 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. dc.identifier.issn 1615-3383 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. dc.format.extent 27 p. dc.language.iso en dc.relation.ispartofseries Foundations of Computational Mathematics. 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/ dc.subject DRNTU::Science::Mathematics::Applied mathematics::Optimization. dc.title The primal-dual second-order cone approximations algorithm for symmetric cone programming. dc.type Journal Article dc.contributor.school School of Physical and Mathematical Sciences dc.identifier.doi http://dx.doi.org/10.1007/s10208-004-0149-7 dc.description.version Accepted version

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