Group Symmetry in Interior-Point Methods for Semidefinite Program

被引：0
作者：
Yoshihiro Kanno
Makoto Ohsaki
Kazuo Murota
Naoki Katoh
机构：
[1] Kyoto University,Department of Architecture and Architectural Systems
[2] Sakyo,Research Institute for Mathematical Sciences
[3] Kyoto University,Department of Mathematical Engineering and Information Physics
[4] Sakyo,undefined
[5] University of Tokyo,undefined
[6] Bunkyo,undefined
来源：
Optimization and Engineering | 2001年 / 2卷
关键词：
semidefinite program; primal-dual interior-point method; group representation theory; structural optimization;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A class of group symmetric Semi-Definite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primal-dual interior-point methods are group symmetric. Preservation of group symmetry along the search direction theoretically guarantees that the numerically obtained optimal solution is group symmetric. As an illustrative example, we show that the optimization problem of a symmetric truss under frequency constraints can be formulated as a group symmetric SDP. Numerical experiments using an interior-point algorithm demonstrate convergence to strictly group symmetric solutions.
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页码：293 / 320
页数：27
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