The primal-dual second-order cone approximations algorithm for symmetric cone programming
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 2 K, a second-order cone ˆKr(x) containing K. We show that K is the interior of the intersection of the second-order cones ˆKr(x), as...
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sg-ntu-dr.10356-1000902023-02-28T19:22:39Z The primal-dual second-order cone approximations algorithm for symmetric cone programming Chua, Chek Beng. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Optimization 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 2 K, a second-order cone ˆKr(x) containing K. We show that K is the interior of the intersection of the second-order cones ˆKr(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. Accepted version 2009-07-28T01:16:03Z 2019-12-06T20:16:32Z 2009-07-28T01:16:03Z 2019-12-06T20:16:32Z 2007 2007 Journal Article Chua, C. B. (2007). The primal-dual second-order cone approximations algorithm for symmetric cone programming. Foundations of computational mathematics, (7)3, 273-302. 1615-3383 https://hdl.handle.net/10356/100090 http://hdl.handle.net/10220/4707 10.1007/s10208-004-0149-7 en Foundations of Computational Mathematics. Foundations of computational mathematics @ copyright 2000 Springer Verlag. The jourmal's websites is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/106038/ 27 p. application/pdf |
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DRNTU::Science::Mathematics::Applied mathematics::Optimization Chua, Chek Beng. The primal-dual second-order cone approximations algorithm for symmetric cone programming |
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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 2 K, a second-order cone ˆKr(x) containing K. We show that K is the interior of the intersection of the second-order cones ˆKr(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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Chua, Chek Beng. |
format |
Article |
author |
Chua, Chek Beng. |
author_sort |
Chua, Chek Beng. |
title |
The primal-dual second-order cone approximations algorithm for symmetric cone programming |
title_short |
The primal-dual second-order cone approximations algorithm for symmetric cone programming |
title_full |
The primal-dual second-order cone approximations algorithm for symmetric cone programming |
title_fullStr |
The primal-dual second-order cone approximations algorithm for symmetric cone programming |
title_full_unstemmed |
The primal-dual second-order cone approximations algorithm for symmetric cone programming |
title_sort |
primal-dual second-order cone approximations algorithm for symmetric cone programming |
publishDate |
2009 |
url |
https://hdl.handle.net/10356/100090 http://hdl.handle.net/10220/4707 |
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1759854990570029056 |