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Invariance and efficiency of convex representations.

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Invariance and efficiency of convex representations.

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dc.contributor.author Chua, Chek Beng.
dc.contributor.author Tunçel, Levent.
dc.date.accessioned 2009-07-28T06:27:56Z
dc.date.available 2009-07-28T06:27:56Z
dc.date.copyright 2006
dc.date.issued 2009-07-28T06:27:56Z
dc.identifier.citation Chua, C. B., & Tunçel, L. (2006). Invariance and efficiency of convex representations. Mathematical Programming, 113-140.
dc.identifier.issn 0025-5610
dc.identifier.uri http://hdl.handle.net/10220/4712
dc.description.abstract We consider two notions for the representations of convex cones: G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation.We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual.We also prove that strict mplementarity of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations.We evaluate the representations of homogeneous convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central path of the represented optimization problem.
dc.format.extent 25 p.
dc.language.iso en
dc.relation.ispartofseries Mathematical programming
dc.rights Mathematical Programming @ copyright 2006 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 Invariance and efficiency of convex representations.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.doi http://dx.doi.org/10.1007/s10107-006-0072-6
dc.description.version Accepted version

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