Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/100091
Title: A new notion of weighted centers for semidefinite programming
Authors: Chua, Chek Beng.
Keywords: DRNTU::Science::Mathematics::Applied mathematics::Optimization
Issue Date: 2006
Source: Chua, C. B. (2006). A new notion of weighted centers for semidefinite programming. SIAM Journal of Optimization, 16(4), 1092–1109.
Series/Report no.: SIAM Journal of Optimization.
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.
URI: https://hdl.handle.net/10356/100091
http://hdl.handle.net/10220/5988
ISSN: 1095-7189
DOI: 10.1137/040613378
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
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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