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Analyticity of weighted central paths and error bounds for semidefinite programming.

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Analyticity of weighted central paths and error bounds for semidefinite programming.

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dc.contributor.author Chua, Chek Beng.
dc.date.accessioned 2009-07-29T09:08:18Z
dc.date.available 2009-07-29T09:08:18Z
dc.date.copyright 2007
dc.date.issued 2009-07-29T09:08:18Z
dc.identifier.citation Chua, C. B. (2007). Analyticity of weighted central paths and error bounds for semidefinite programming. Mathematical Programming, 239-271.
dc.identifier.issn 0025-5610
dc.identifier.uri http://hdl.handle.net/10220/5855
dc.description.abstract The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semi definite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of strictly complementary solutions. Secondly, we consider a sequence of primal-dual solutions that lies within a prescribed neighborhood of the central path of a pair of primal-dual semi definite programming problems, and converges to the respective optimal faces. Under the additional assumption of strict complementarity, we derive two necessary and sufficient conditions for the sequence of primal-dual solutions to converge linearly with their duality gaps.
dc.format.extent 28 p.
dc.language.iso en
dc.relation.ispartofseries Mathematical programming
dc.rights Mathematical Programming @ copyright 2007 Springer-Verlag. The journal's website is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/103081.
dc.subject DRNTU::Science::Mathematics::Applied mathematics::Optimization.
dc.title Analyticity of weighted central paths and error bounds for semidefinite programming.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.doi http://dx.doi.org/10.1007/s10107-007-0155-z
dc.description.version Accepted version

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