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Chek Beng Chua (cbchuamath.uwaterloo.ca) Abstract: This paper presents the new concept of secondorder cone approximations for convex conic programming. Given any open convex cone $K$, a logarithmically homogeneous selfconcordant barrier for $K$ and any positive real number $r \le 1$, we associate, with each direction $x \in K$, a secondorder cone $\hat K_r(x)$ containing $K$. We show that $K$ is the intersection of the secondorder cones $\hat K_r(x)$, as $x$ ranges through all directions in $K$. Using these secondorder cones as approximations to cones of symmetric positive definite matrices, we develop a new polynomialtime primaldual interiorpoint algorithm for semidefinite programming. The algorithm is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras. Keywords: semidefinite programming, symmetric cone, interiorpoint methods, secondorder cones Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: Foundation of Computational Mathematics, 7 (2007), 271302 Download: Entry Submitted: 03/03/2003 Modify/Update this entry  
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