Abstract
Given any open convex cone K, a logarithmically homogeneous, self-concordant barrier for K, and any positive real number r < 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 interior of the intersection of the second-order cones \(\Hat K_r(x)\), as x ranges over 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 semidefinite programming. The algorithm is extended to symmetric cone programming via the relation between symmetric cones and Euclidean Jordan algebras.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chua, C. The Primal-Dual Second-Order Cone Approximations Algorithm for Symmetric Cone Programming. Found Comput Math 7, 271–302 (2007). https://doi.org/10.1007/s10208-004-0149-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10208-004-0149-7