- A primal-dual second order cone approximations algorithm for symmetric cone programming Chek Beng Chua (cbchuamath.uwaterloo.ca) Abstract: This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone $K$, a logarithmically homogeneous self-concordant barrier for $K$ and any positive real number $r \le 1$, we associate, with each direction $x \in K$, a second-order cone $\hat K_r(x)$ containing $K$. We show that $K$ is the intersection of the second-order cones $\hat K_r(x)$, as $x$ ranges through 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 semi-definite programming. The algorithm is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras. Keywords: semi-definite programming, symmetric cone, interior-point methods, second-order cones Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: Foundation of Computational Mathematics, 7 (2007), 271-302 Download: Entry Submitted: 03/03/2003Entry Accepted: 03/03/2003Entry Last Modified: 09/10/2008Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.